Problems
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- Prove that \[ \frac{d}{dx}x^n=nx^{n-1} \]using the Binomial Theorem where $n$ is a positive integer.
- Determine the derivative of $f(x)=\sqrt{x}$.
- Derivative of $f(x)=-x^2$
- The derivative of $x^3$.
- Prove that $f(x)=|x|$ is not differentiable at $x=0$.
- The derivative of $f(x)=mx+b$.
- Prove that $f(x)$ is differentiable at $x$ if and only if \[ \lim_{t\to x}\,\frac{f(t)-f(x)}{t-x} \] exists. When the limit exists it is equal to $f'(x)$.
- Find the derivative of $f(x)=x$.
- The Derivative of a Constant
- Derivative of $x^2$
