IB Mathematics Applications & Interpretation Question Type 6: Deriving Functions by Applying Product, Quotient and Chain Rule Exercises

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

Differentiate $f(x)=\frac{e^x\sin x}{x^2}$.

Find the derivative of the function $f(x)=x\sin (\sqrt{x})$.

Find the derivative of $f(x)=e^{3x}\cos (x^2)$.

Differentiate $f(x)=\frac{\sin x}{x^2}$.

Compute $\frac{d}{dx}\left(\frac{\cos (\ln x)}{x}\right)$.

Find $\frac{\text{d}}{\text{d}x}\left(\frac{{\text{e}}^x}{1+{\text{e}}^x}\right)$.

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

Differentiate the function $f(x)=\frac{\cos (\ln x)e^{-x}}{x\ln x}$.

Differentiate $f(x)=\frac{\ln (x)}{x}$.

Find the derivative of $f(x)=e^{-x}\ln (\cos x)$.

Find $f^{\prime }(x)$.