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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 $x^2$

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Lesson Specific Problems

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 $x=0$ .

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