Question

How do you differentiate `f(x)=arctanx*3x` using the product rule?

Answer 1

`d/dxf(x) = (3x)/(1+x^2) + 3arctanx`

Explanation:

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Differentiating `f(x)` is determined by applying product differentiation.
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Product Differentiation:
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`color(blue)(d/dx(u(x)xxv(x))=d/dxu(x)xxv(x) + u(x)xxd/dxv(x))`
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`d/dxf(x) = d/dx((arctanx)xx3x)`
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`d/dxf(x) = d/dx(arctanx)xx3x + arctanx xx d/dx(3x)`
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`d/dxf(x) = 1/(1+x^2)xx3x + arctanx xx 3`
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`d/dxf(x) = (3x)/(1+x^2) + 3arctanx`