184 Answered Questions for the topic Differentiation

Differentiation Triangles Parabola


Find the maximum area of a triangle underneath a parabola

An Isosceles triangle ABC is embedded in the parabola y=x(4-x). C is always at the point (2,0) while A and B are at the same but variable height above the x-axis. Find the maximum area of ABC.I... more
Differentiation Math Calculus


Estimate height using position-function

To estimate the height of a building, a stone is dropped from the top of the building into a pool of water at ground level. How high is the building if the splash is seen 6.9 seconds after the... more
Differentiation Mathematics


Find dy/dx of the following question

Find 𝑑𝑦/𝑑𝑥 for the following 𝑥2 = 𝑦2 + sin 𝑥𝑦


Let y be defined implicitly by the equation ln(8y)=5xy.

A) Use implicit differentiation to find the second derivative of y with respect to x. ((d^2)y)/(d(x^2)= ? Note: Your answer should only involve the variables x and y. You should simplify your... more
Differentiation Calculus Continuous Functions


Determine the values of a and b which would result in the function f(x) being differentiable at x=2.

f(x) = { 2ax + 10 x<or equal to 2 { bx^2 - 4x + 9 x>2





My Cal question

Find an equation of the tangent line to the curve y = x ^4 + 1 that is parallel to the line y = 32x − 15
Differentiation Calculus


Hi i need help solving the following

A line is drawn through the point P(3, 4) so that it intersects the y‐axis at A(0, y) and the x‐axis at B(x, 0). Find the smallest area of triangle formed if x and y are positive.
Differentiation Calculus Precalculus


Differentiation:The Chain Rule

Given:f(2)=1f(8)=5f'(2)=7f'(8)=-3What is g(2) if g(x) = [f(x)]³
Differentiation Calculus Derivative


Graphical Interpretation of the derivatives

Just started a new topic, need a little help with the following:The graph of the function y=x^3+ax^2+bx+c passes through (1,1) and has turning points at x= -1 and x= 3. Find the values of a, b and c
Differentiation Math Calculus Highschool


Rules for Differentiation (Highschool Calculus)

Find the values of a and b so that g(x) is both continuous and differentiable at x=0.g(x){ ax+b, x > 0 1-x+x2, x (< and/or =) 0


At what rate is the water level rising?

A swimming pool is 20 m long, 5 meters wide, has sides in the shape of a right triangle, and slopes downward so that it is 4 meters deep at the deep end. Water is being pumped into the pool at 2m^3... more
Differentiation Math Calculus Functions


Help Solving Calculus Problem

An apple farm yields an average of 39 bushels of apples per tree when 21 trees are planted on an acre of ground. Each time 1 more tree is planted per acre, the yield decreases by 1 bushel (bu) per... more


Theory of partial differentiation

WHY A TOTAL DIFFERENTIATION CAN BE RECIPROCAL BUT PARTIAL DIFFERENTIATION CANNOT BE RECIPROCALed?EX if (dx/dy)=sinp then (dy/dx)=cosecp BUT in case of partial differentiation... more
Differentiation Calculus


Suppose h = f∘g. Find h'(0)

Given that f(0) = 5 f '(5) = -7 g(0) = 5 g '(0) = 4  


Differentiation - Chain Rule

A cone-shaped container with a hole at its top vertex is filled with water. The cone has a 4cm radius and 16cm in height. The cone was turned upside down to the let its water flow out of container.... more
Differentiation Math Math Help


Differentiation - are these answers correct?

Could someone help me check if I differentiated these these two functions correctly:   f(x)= √(3x2-x3)   And   h(x) = 3√(5x+x2)2     I got: f′(x) = 6x-3x2/2·√(3x2-x3)   And   h′(x) =... more
Differentiation Math Derivatives


Derivatives - local extremes

f(x) = x3 - 8x2 + 5x   Compute algebraically the x-coordinates of the points on the graph of f where the tangent to this graph is horizontal.    I know how to find the derivative:   f′(x) =... more


Implicit Differentiation

x2y2 +y+1=0 
Differentiation Math


Differentiation - Help for exam prep!

Differentiate the following function and simplify.   h(x) = x2 · √8-x     Answer = 2x√8-x - x/2√8-x   Could you show me the step by step process and which rules to use in order to... more
Differentiation Math Product Rule



y= -x5(1 - x)   I have to use the product rule to answer this question.    The answer is 6x5 - 5x4   Can someone explain this to me and show how to solve it?   Thank you so much!

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