IB Mathematics Analysis and Approaches Question Type 7: Learning to Apply All the Rules, Product, Chain and Quotient Together for Any Derivatives of Composite Functions of x Exercises

Differentiate $f(x)=\frac{x^2\sec \left(\sqrt{\ln x}\right)}{1+x{e}^{-x}}$ for $x>1$.

Differentiate $f(x)=\frac{x^2{e}^{\sin x}}{\sqrt{1+x^2}}$.

Differentiate $f(x)=\frac{(1+\ln x)e^{x^2}}{\cos x}$ for $x>0$.

Differentiate $f(x)=\frac{\sin (\ln (x^2+1))}{x{e}^x}$.

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

Differentiate $f(x)=\frac{e^{-x}\cos (\ln x)}{x\ln x}$ for $x>0$, $x\ne 1$.

Differentiate $f(x)=\frac{(\ln x{)}^3}{e^x\cos (\ln x)}$ for $x>0$ by rewriting as a product.

Differentiate $f(x)=\ln \left(\frac{\sin (x^3)}{x{e}^x}\right)$ for $x>0$.

Differentiate $f(x)=\frac{x\arctan (\sqrt{x})}{\ln x}$ for $x>0$, $x\ne 1$.

Differentiate $f(x)=(\ln x{)}^2\tan (x^2)$ for $x>0$.

Differentiate $f(x)=\frac{\sqrt{\ln (1+x^2)}}{x\sin x}$ for $x>0$ and $x\ne k\pi$ where $k\in \mathbb{Z}$.

Differentiate $f(x)=\left(x+\frac{1}{x}\right)e^{-\ln (\cos x)}$ on intervals where defined.