What is the derivative of f(x(5x^2-4)) ?

The derivative of f(x(5x^2-4)) is derivative of {f}(x)(5x^2-4)+10x{f}(x)

What is the first derivative of f(x(5x^2-4)) ?

The first derivative of f(x(5x^2-4)) is derivative of {f}(x)(5x^2-4)+10x{f}(x)

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\frac{d}{d x} (f (x) (5 x^{2} - 4))

\frac{d}{d x} (f (x)) (5 x^{2} - 4) + 10 x f (x)

Solution steps

\frac{d}{d x} (f (x) (5 x^{2} - 4))

Apply the Product Rule:

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

f = f (x), g = 5 x^{2} - 4

= \frac{d}{d x} (f (x)) (5 x^{2} - 4) + \frac{d}{d x} (5 x^{2} - 4) f (x)

\frac{d}{d x} (5 x^{2} - 4) = 10 x

= \frac{d}{d x} (f (x)) (5 x^{2} - 4) + 10 x f (x)

\int \frac{8 e ^{- \frac{1}{x}}}{x ^{2}} d x

- \frac{6}{( 1 - x ) ^{4}}

\frac{d ^{2}}{d x ^{2}} ((- 6 - 7 t)^{6})

\int_{1}^{4} t d t

y^{^{'}} = e^{y + 2 x}

What is the derivative of f(x(5x^2-4)) ?
The derivative of f(x(5x^2-4)) is derivative of {f}(x)(5x^2-4)+10x{f}(x)
What is the first derivative of f(x(5x^2-4)) ?
The first derivative of f(x(5x^2-4)) is derivative of {f}(x)(5x^2-4)+10x{f}(x)