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Popular >

derivative of {f}(x(x)^2(x))

Solution

\frac{d}{d x} (f (x) (x)^{2} (x))

Solution

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

Solution steps

\frac{d}{d x} (f (x) (x)^{2} (x))

Simplify

f (x) (x)^{2} (x) : x^{3} f (x)

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

Apply the Product Rule:

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

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

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

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

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

Popular Examples

integral from 1/3 to 5 of 16xln(3x)

\int_{\frac{1}{3}}^{5} 16 x ln (3 x) d x

tangent of f(x)=x^2+4x-5,\at x=2 tangent of

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

derivative of nln(x)

\frac{d}{d x} (n ln (x))

integral of 1/(25-81x^2)

\int \frac{1}{25 - 81 x ^{2}} d x

integral of ((x^3+x))/(2x-1)

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

Frequently Asked Questions (FAQ)

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