Differentiation

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Differentiation is an important part of calculus.

If $y=f(x)$ , then differentiating y with respect to x will give the gradient function of a curve, or if $y=f(x)$ is a straight line $\frac{dy}{dx}$ is equal to the gradient.

The general rule for differentiation of a power function is:

If $y=ax^n$ then $\frac{dy}{dx}=anx^{n-1}$

The chain rule, product rule, and quotient rule are used when differentiating more complicated functions. Some functions, however, cannot be differentiated algebraically so numerical solutions and iterative methods are required to approximate $\frac{dy}{dx}.$