Differentiation
JUPEB Mathematics

Differentiate $y = 3x^4 - 2x^2 + 5$ with respect to $x$.

Find $\dfrac{dy}{dx}$ if $y = \sin 3x$.

Find the gradient of the curve $y = x^3 - 3x$ at the point where $x = 2$.

Differentiate $y = x^2 e^x$ with respect to $x$.

Find the coordinates of the minimum point of the curve $y = x^3 - 6x^2 + 9x$.

Differentiate $y = \ln(x^2 + 1)$ with respect to $x$.

Find $\dfrac{dy}{dx}$ if $y = \dfrac{2x + 1}{x - 1}$.

Find the equation of the tangent to the curve $y = x^2$ at the point $(2, 4)$.

The radius of a circular oil spill is increasing at the rate of $2$ cm s$^{-1}$. Find the rate at which the area is increasing when the radius is $5$ cm.

If $y = x^4 - 2x^3$, find the value of $\dfrac{d^2y}{dx^2}$ when $x = 1$.

Given that $x^2 + y^2 = 25$, find $\dfrac{dy}{dx}$ at the point $(3, 4)$.

Differentiate $y = \tan^2 x$ with respect to $x$.