What is the derivative of f(x(5x^2+3)) ?

The derivative of f(x(5x^2+3)) is derivative of {f}(x)(5x^2+3)+10x{f}(x)

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

The first derivative of f(x(5x^2+3)) is derivative of {f}(x)(5x^2+3)+10x{f}(x)

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

\frac{d}{d x} (f (x)) (5 x^{2} + 3) + 10 x f (x)

Solution steps

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

Apply the Product Rule:

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

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

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

\frac{d}{d x} (5 x^{2} + 3) = 10 x

= \frac{d}{d x} (f (x)) (5 x^{2} + 3) + 10 x f (x)

\int x^{3} x^{4} + 10 d x

4 y^{^{''}} + 4 y^{^{'}} + 9 y = 0

\int_{2}^{3} \frac{1}{x ^{2} - 1} d x

\int (y - 2)^{2} d y

\frac{d}{d x} (\frac{( x ^{2} - 5 ) ^{3}}{x ^{2} + 4})

What is the derivative of f(x(5x^2+3)) ?
The derivative of f(x(5x^2+3)) is derivative of {f}(x)(5x^2+3)+10x{f}(x)
What is the first derivative of f(x(5x^2+3)) ?
The first derivative of f(x(5x^2+3)) is derivative of {f}(x)(5x^2+3)+10x{f}(x)