Find {eq}f'(x), {/eq} if {eq}f(x) = x^3 \cot x. {/eq}


Find {eq}f'(x), {/eq} if {eq}f(x) = x^3 \cot x. {/eq}

Product rule of differentiation:

Assume that {eq}u {/eq} and {eq}v {/eq} be two differentiable functions, then their product {eq}(uv) {/eq} is also differentiable,

The derivative of that product {eq}uv {/eq} is {eq}u'v + v'u {/eq}.

And also know that the derivative of {eq}x^n {/eq} is {eq}nx^{n - 1} {/eq}, where {eq}n {/eq} is a real number.

Answer and Explanation: 1

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$$f(x) = x^3 \cot x $$

Differentiate the given function with respect to {eq}x {/eq},

$$\displaystyle \begin{align*} f'(x) &= \dfrac...

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Product Rule in Calculus: Formula & Examples


Chapter 10 / Lesson 14

Understand what the product rule is. Learn about the product rule in calculus. Know about the derivative multiplication rule and the product rule equation.

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