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Popular >

derivative of f(x(3x^2+5))

Solution

\frac{d}{d x} (f (x) (3 x^{2} + 5))

Solution

\frac{d}{d x} (f (x)) (3 x^{2} + 5) + 6 x f (x)

Solution steps

\frac{d}{d x} (f (x) (3 x^{2} + 5))

Apply the Product Rule:

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

f = f (x), g = 3 x^{2} + 5

= \frac{d}{d x} (f (x)) (3 x^{2} + 5) + \frac{d}{d x} (3 x^{2} + 5) f (x)

\frac{d}{d x} (3 x^{2} + 5) = 6 x

= \frac{d}{d x} (f (x)) (3 x^{2} + 5) + 6 x f (x)

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Frequently Asked Questions (FAQ)

What is the derivative of f(x(3x^2+5)) ?
The derivative of f(x(3x^2+5)) is derivative of {f}(x)(3x^2+5)+6x{f}(x)
What is the first derivative of f(x(3x^2+5)) ?
The first derivative of f(x(3x^2+5)) is derivative of {f}(x)(3x^2+5)+6x{f}(x)