Calculus Derivatives

Partial Derivative

100

f(x,y)=y³x² 

Calculate ∂f/∂x

2y³x

200

f(x, y, z) = x⁴ − 3xyz

calculate ∂f/∂x, ∂f/∂y, and ∂f/∂z

∂f/∂x = 4x³ − 3yz

∂f/∂y = −3xz

∂f/∂z = −3xy

300

f(x, y) = (4x+9)(8x+5y)

calculate ∂f/∂x and ∂f/∂y

∂f/∂x = 64x +20y +72

∂f/∂y =20x +45

Product and Quotient Rule

100

Find the derivative of 

f(x) = (3x - 2x²)(5 + 4x)

-24x² + 4x + 15

200

Find the derivative of

 y = (5x - 2)/(x² + 1)

(-5x² + 4x + 5)/(x² + 1)²

300

Find the derivative of f(x) = (2x + 5)/(x)^1/2

(2x - 5)/(2x^3/2)

Chain Rule

100

Find derivative of 

f(x) = (3x - 9)⁴

12(3x - 9)³

200

Find derivative of (6x²+7x)⁴

4(6x²+7x)³(12x+7)

300

Find derivative of 

f(x)=1/(3x-2)

-3/(3x-2)²

Implicit Differentiation

100

Find the derivative implicitly

x² + y² = 30

- x/y

200

Find the derivative implicitly 

(y - 2)² = 4x - 12

2/(y - 2)

300

x³ - 3x²y + 2xy² = 12

(-3x² + 6xy - 2y²)/(-3x² + 4xy)