287 Answered Questions for the topic Derivatives

Derivatives Calculus 1

05/03/18

#### Given f(x) = x^2 if x<1 and ax^2+bx +c if x ≥ 1 find the values of a and b such that f` (1) exists?

find the values of derivatives, anyone who can help me to solve this problem welcome!!

Derivatives Business Calculus

04/16/18

#### Find the equation of the tangent to the graph at the indicated point.

x^2-6x; a=-1

Derivatives

04/16/18

#### find the derivative of an equation

can you please help me find the derivative of x^2+(y-5)=25

Derivatives Trajectory

04/15/18

#### if the trajectory of a stone is modeled by d=37+7t-4.9t^2 What is the speed of the stone after 2 sec?

If the trajectory of a stone is modeled by d=37+7t-49t^2, where t is the time in seconds and d is the vertical distance in meters.
What is the speed of the stone after 2 seconds?

#### Assume s,v, and a are continuous functions and s is twice differentiable, where s(t) represents the position, v(t) is velocity, a(t) is acceleration

Find the following:
d/dx of integral from t to t^2 of v(w)dw
integral from t to t^2 of v(w)dw
second derivative of integral from t to t^2 of v(w)dw
Calculus question I am stuck on

Derivatives

03/26/18

#### What is the first derivative of 3\sqrt[3]{x^4}-12\sqrt[3]{x}?

3\sqrt[3]{x^4}-12\sqrt[3]{x}
Im trying to get critical points for the equation, but im getting very confused on what the correct 1st derivative is.

03/24/18

#### Differential Equation Problem. No clue how to do this.

Find the derivatives of each of the following vectors.
x(t) = [ t3 - 2t2 +t
etsin(t) ]

Derivatives Even Functions

03/20/18

#### even function with negative first derivative?

I'm pretty sure this scenario is impossible but want to check for sure. I have been asked to graph an even function whose first derivative is negative on the interval (-2,2). Impossible right?

Derivatives

03/20/18

#### Let f and g be functions that satisfy f'(2)=-12 and g'(2)=-1, Find h'(2) for the following

I am not sure what to do if I am not given the f(2) value and g(2) value! The functions are as follows
1. h(x)=6f(x)
h'(2)=_____
2. h(x)=-5g(x)
h'(2)=_____
Please help!!!!

Derivatives Calculus

03/20/18

#### Second derivative of y relative to x^2

y = cos(t)
t = sin(x)
for x =π what's the value of d2y over dx2

Derivatives Related Rates

03/18/18

#### related rates help please!!

A spherical balloon is being inflated so that its volume is increasing at the rate of 10cm3/sec. Find the rate at which the diameter is increasing when the diameter is 20cm?

#### Radius (r) of sphere is expanding at rate of 9cm/min. Volume of sphere is V=4/3(pi(r^3))

Determine the rate at which the volume is changing with respect to time when r=8cm. (in cm^3/min)

#### How can I transform −λ△t= (N(t+△t)−N(t)) / (△t) into the formula dN/dt=−λN using limits?

How can I transform −λ△t= (N(t+△t)−N(t)) / (△t) into the formula dN/dt=−λN using limits? This is in relation to radioactive decay for those that are wondering, thank you for your help and time!...
more

03/11/18

#### A car leaves an intersection traveling west. Its position 4 sec later is 22 ft from the intersection. At the same time, another car leaves the same intersection

A car leaves an intersection traveling west. Its position 4 sec later is 22 ft from the intersection. At the same time, another car leaves the same intersection heading north so that its position 4...
more

03/11/18

#### Second derivative

Find the second derivative d2y/dx2 of the function defined implicitly by the equation.x1/3 + y1/3 = 94d2y/dx2 = ___________

03/02/18

#### Distance traveled derivative

The distance S covered by a car after t sec is given by: s=-t3 + 8t2 +20t (0≤t≤6)
Find the general expression for the car's acceleration at any time t (0≤t≤6). Show that the car is decelerating...
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#### Find each limit by evaluating the derivative of the function

Find each limit by evaluating the derivative of the function
limh→0 ((3(2+h)2-(2+h)-10))/h

Derivatives Logarithic Differentiation

02/27/18

#### Derivative of y=sqrt(x(x+1))/(e^x((x^2)+2)) using logarithmic differentiation.

The whole equation is under the square root. Thanks.

Derivatives

02/17/18

#### derivative of (am/(am+n))^m wrt m

My guess is
y=(am/(am+n))^m
F.O.C wrt m
lny = m* ln(am/(am+n)) (ln on both sides)
1/y * y'= ln(am/(am+n) + m*((am+n)/am)*(a(am+n)-am(a))/(am+n)^2 (chain rule on left hand side, product...
more

Derivatives

02/17/18

#### 1. The functionf: R→ R is differentiable and f(−5) = f(9) = 0. Then the function g(x)=cos(f(x)) satisfies the condition:

A) g′ has at least 3 zeroes
B) g′ has at most one zeroes
C) g′ has at exactly 3 zeroes
D) g′ has an infinite number of of zeroes

Derivatives Calculus

02/11/18

#### Evaluate the derivative using logarithmic differentiation?

y=(x3+1)(x4+7)(x5+8)4

Derivatives Calculus

02/11/18

#### Evaluate the derivative using logarithmic differentiation?

y=x(x5+4)/√x+4

#### Tangent line is horizontal

Let f(x) = x3 − 4x2.
Find the point(s) on the graph of f where the tangent line is horizontal.(x, y) =____________ (smaller x-value)(x, y) =____________ (larger x-value)

Derivatives Limits

02/08/18

#### Use the Limit Definition of the Derivative to find derivative of f(x)=1/sqrt(9x)

Confused on how to do the Definition of A Derivative.

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