Question Type 4: Deriving functions with a combination of product and chain rule Exercises

Differentiate the function $f(x) = \sin(e^x + x^2) \ln(x^2 + 1)$.

Find the derivative of $f(x) = (\ln x)^3 \sin(x^2)$.

Find $\frac{d}{dx}[e^{x^2}\cos(x^3)]$.

Differentiate the function $f(x) = (3x + 1)^4 \sqrt{x^2 + 2x}$.

Compute the derivative of $f(x) = x e^{\sqrt{x}}$.

Differentiate $f(x) = \tan^2(x^2)e^{3x}$.

Find $f'(x)$.

Differentiate $f(x) = \ln(5x) \sqrt{x^2 + 1}$.

Compute $\frac{d}{dx} \left[ \ln(\sin(x^2)) e^x \right]$.

Find the derivative of $f(x) = \sin x \cdot e^{x^2} \cdot \ln x$.

Differentiate $f(x) = e^{\tan x} x^3$ with respect to $x$.

Compute the derivative of $f(x) = (x^2-1)^3 e^{2x+1}$.