Derivatives Using Power Rule

Find the derivative of the given equation

f(x) = x⁴ + 4x³ - 2x²

• f'(x) = x³ + x² - x

• f'(x) = 4x³ + 12x² + 4x

• f'(x) = 4x + 12x - 4x

• f'(x) = 4x³ + 12x² - 4x

What is the derivative of a constant, c?

• c

• 0

• 1

If a is a constant, what is the derivative of ax?

• a

• x

• 1

• 0

Find the derivative of the given equation
 $f\left(x\right)=\frac{1}{x^2}$ . Hint: Rewrite with a negative exponent first! 

•  $f'\left(x\right)=\frac{1}{2x}$  

•  $f'\left(x\right)=-2x^3$  

•  $f'\left(x\right)=2x$  

•  $f'\left(x\right)=-\frac{2}{x^3}$  

Find the derivative of the given equation

y = 7

• y' = 7

• y' = 0

• y' = 7x

• y' = 14

Find the derivative of the given equation

g(x) = 1 - x²

• g'(x) = 1 - 2x

• g'(x) = -2x

• g'(x) = -2

• g'(x) = -1

Find the equation of the gradient of the tangent line to  $y=-3x^2-11x$  

What is the derivative of xⁿ?

• (n-1)xⁿ

• nxⁿ⁺¹

• nx^n-1

• (n+1)x^n-1

Differentiate y = 12x^-2

Differentiate  $y=\frac{2x^2+3x-4}{x}$  . SIMPLIFY first by dividing each term in the numerator by the denominator.