Differentiating Function Equation

A method for finding the derivative of an implicitly defined function or relation in which the dependent variable is not isolated on one side of the equation

• Implicit Equation

• Explicit Equation

• Explicit Differentiation

• Implicit Differentiation

To say that a function f is differentiable at x means that

• f'(x) exists

• f'(x) doesn't exist

• f(x) exists

• f(x) doesn't exist

The rate at which one quantity is changing by relating it to other quantities whose rates are known

• Average Rate of Change

• Instantaneous Rate of Change

• Rate of Change

• Related Rates

Find the derivative
f(t) = (t² + 2t)⁵

• f'(t) = 5(2t+2)⁴

• f'(t) = 5(t² + 2t)⁴

•  f'(t) = 5(t² + 2t)⁴(2t)

• f'(t) = 5(t² + 2t)⁴(2t + 2)

Find dy/dx for y = 4x³ + 3x + 1

• dy/dx = 4x² + 3

• dy/dx = 4x² + 3x

• dy/dx = 12x² + 3x

• dy/dx = 12x² + 3

Differentiate (2x + 2)(x - 5)⁸ with respect to x.

• (2x + 2)(x - 5)⁷ + 2(x - 5)⁸

• 8(2x + 2)(x - 5)⁷ + 2(x - 5)⁸

• 2(x - 5)⁸

• 16(x - 5)⁷

Find the derivative of the given equation
f(x) = x³ + x² + 3

• 3x² + 2x

• 3x + 2x 

• 3x + 2x + 3

• x³ + x² 

What is the mathematical definition of the product rule?

• 
• 
• 

Let y = (x - 1)(x + 2). Find dy/dx.

• 2x + 1

• 2x - 1

• 4x - 1

• 2x² + x - 1

• 
• 
• 
•