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

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

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

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

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

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

Find $f'(x)$ if $f(x)=\\sqrt{\\sin x}\\ln x$.

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

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

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

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

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

Differentiate $f(x)=(\\ln x)^3\\sin(x^2)$.