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287 Answered Questions for the topic Derivatives

Derivatives Calculus Limits


L HOPITALS and derivative

ive got 3 questions   lim x approaches positive 1 (sq rt of x^2 - 1) / (arcsecx)   lim x approaches 0  2arctan3x^2 / 7x^2     initial value prob   dy/dx=1/(x^2+1) -1     I NEED HELP... more
Derivatives Calculus Calculus 1


Find all the second partial derivatives of the function below. (Hint: there are 4)

Having difficulty finding them I can only find one       ??(??,??)=2??^5 ??^2+??^2 ??

What is application of derivatives in atual life

If y=eloge(log x)2                Fine    dy/dx .          What is used of ??sum in atual life 


If y=x^3+3x and dx/dt=7. Find dy/dt when x=4.

If y=x^3+3x and dx/dt=7. Find dy/dt when x=4.
Derivatives Calculus


find the derivative?

Derivatives Calculus


given f(x)=x^8h(x) and h(x)=2 and h'(x)=5, find f'(-1)

it says to use the power rule as well as the product rule. i know how both of those rules work but not how they work into this particular problem.


Find dy/dx by implicit differentiation

tan³(xy²+y) = x
Derivatives Calculus 1


Find an equation for the tangent line to the graph at the specified value of x

1 - y = xcos3x; x = π   2 - y = sec 3 (π/2 - x); x = -π/2   3 - y = Tan(4x 2  ); x = √π     Hey guys please help me with these ones, i am studying for finals, if possible try to solve them... more
Derivatives Pre Calculus



If f(x)=8x^3-2x-6, approximate the derivative at x=2 using a forward difference approximation of (f(x+0.01)-f(x))/0.01   f'(2)=?????    Would you please explain how to solve this problem? 
Derivatives Graphs Of Functions


Derivatives & the Shapes of Graphs

1. Answer the questions below based on the following information about the function f . You must justify youranswers.(i) The function f is continuous and differentiable for all values of x.(ii)... more



I need help answering this word problem...I need to find the function P(t) and I just can't remember the process whatsoever   "A company has its profit function P(t) defined since its inception... more
Derivatives Word Problem Calculus 1


Could someone help me with this calculus rate problem?

Water is leaking out of an inverted conical tank at a rate of 10100.0 cm3/min at the same time that water is being pumped into the tank at a constant rate. The tank has height 9.0 m and the the... more


Finding two part derivative/tangent line

So I'm supposed to graph the given function at the tangent line at the given point, which I know how to do with an explicit/one part function but not an implicit/two part function.The function... more


find derivative---

Derivatives Calculus Algebra


Finding numeric values of variables A & B from an equation

An amusement park designs a roller-coaster ride based on the function f(t)=at^2-bt+20, where t is the time of the ride in seconds. The designer wants to achieve the speed f'(1)=10 mph, and... more


The Derivative

Compute The Derivative of the given function and find the equation of the tangent line that is tangent to it's graph for the specified value x=c14.) f (x) = 3; c= -416.) f(x) = 3x; c=1   find the... more


derivative of y=x^3sinxcosx

im confused because these are three products dont know how to use chain rule or product rule with it pls show step by step procedure thanks


Differentiate the Given function. Simplify the Answer and show solution:

18.) f(x) = 1/4 x^8 - 1/2 x^6 - x +2 and 20.) f(u) = 0.07u^4 - 1.21u^3 +3u - 5.2   210) f(x) = (x+1/x)^2Thank you your a blessing God bless.
Derivatives Calculus 1


I'm not allowed to use the Chain rule in my midterm, what else can I do to find the derivative of f(g(x)) functions?

I am quite puzzled because I was just told by my professor that we won't be allowed to use the Chain rule in the exam, but in the practise exam they gave us functions like y=e^3x+x to... more
Derivatives Calculus 1


F'(x) = t'^4/4-t^3+t^2

pls help me find the derivative thanksss
Derivatives Calculus 1


Find the derivative of r = 2(1/sqrt theta + sqrt of theta)

i got -1/theta(sq rt of theta) + 2 sq rt of theta howeverrrrr back of the book says 1/theta sq rtof theta + 1/2 sq rt of theta. Pls help and show solution please!
Derivatives Calculus 1


Find the 1st and second derivative of y=x^3/3+x^2/2+x/4

My answer is x^2/9+x/4however back of the book says x^2+x
Derivatives Calculus Limits


Let f(x)= x^1/2. Find f'(9) using the definition f'(a)=limex->a f(x)-f(a)/x-a

I am stuck can you please help?   So far I have limx->9√x-√9                               x  -9                               =x(x^-1/2)-(3/x)                              ... more
Derivatives Calculus Chain Rule


Using chain rule and product/quotient rule, find derivative of sin(3x^2)/x when x=(squareroot of pi)

sin(3x^2)x^-1   this is how far I got.  when do I sub in √pi ? what do I do next?


The expression f(a+h)-f(a)/h is called the

a)instantaneous rate of change of f at a b) difference quotient of f at a c)definition of f'(a) d)secant line of f at a   I tried a) and c) but they're wrong.   What is it supposed to be?
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