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Popular >

derivative of {f}(x(x^3+x-3))

Solution

\frac{d}{d x} (f (x) (x^{3} + x - 3))

Solution

\frac{d}{d x} (f (x)) (x^{3} + x - 3) + (3 x^{2} + 1) f (x)

Solution steps

\frac{d}{d x} (f (x) (x^{3} + x - 3))

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = f (x), g = x^{3} + x - 3

= \frac{d}{d x} (f (x)) (x^{3} + x - 3) + \frac{d}{d x} (x^{3} + x - 3) f (x)

\frac{d}{d x} (x^{3} + x - 3) = 3 x^{2} + 1

= \frac{d}{d x} (f (x)) (x^{3} + x - 3) + (3 x^{2} + 1) f (x)

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Frequently Asked Questions (FAQ)

What is the derivative of {f}(x(x^3+x-3)) ?
The derivative of {f}(x(x^3+x-3)) is derivative of {f}(x)(x^3+x-3)+(3x^2+1){f}(x)
What is the first derivative of {f}(x(x^3+x-3)) ?
The first derivative of {f}(x(x^3+x-3)) is derivative of {f}(x)(x^3+x-3)+(3x^2+1){f}(x)