IB Mathematics Analysis and Approaches Question Type 2: Derivatives from First Principles Exercises

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

Using first principles, find the derivative of $f(x)=\frac{1}{\sqrt{x}}$.

Using first principles, find the derivative of $f(x)=x^2+1$.

Using first principles, find the derivative of $f(x)=x^5$.

Using first principles, find the derivative of $f(x)=3x+2$. [4]

Using first principles, find the derivative of $f(x)=\sqrt{x}$.

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

Using first principles, find the derivative of $f(x)=5x^4$.

Using first principles, find the derivative of $f(x)=x^3$.

Using first principles, find the derivative of $f(x)=2x^2-x$.

Using first principles, find the derivative of $f(x)=\frac{1}{x}$.