Question Type 2: Computing harder derivatives from first principles Bootcamps

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

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

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

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

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

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

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

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

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

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

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

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