Question Type 2: Computing harder derivatives from first principles Exercises

Using the first principles definition, compute the derivative of $f(x)=\cos x \sin x$.

Using the definition of the derivative, find $f'(x)$ for $f(x)=x^2 \ln x$ for $x>0$.

Using first principles, find $f'(x)$ for $f(x)=x^2 e^{-x}$.

Using the definition of the derivative, compute $f'(x)$ for $f(x)=x^3 \cos x$.

Using first principles, compute the derivative of $f(x)=\cos^2 x$.

Find $f'(x)$ for $f(x)=\sin^2x$ from first principles.

Find $f'(x)$ for $f(x)=x e^x$ using the definition of the derivative.

Using first principles, find the derivative of $f(x)=\frac{\sin x}{x}$ for $x\neq0$.

Using the definition of the derivative (first principles), find $f'(x)$ for $f(x)=x \sin x$.

Using first principles, find the derivative of $f(x)=\ln(x)\sin x$ for $x>0$.

Using first principles, compute the derivative of $f(x)=e^x \sin x$.

Using first principles, find $f'(x)$ for $f(x)=x^2 \cos x$.