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Popular >

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

Solution

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

Solution

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

Solution steps

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

Simplify

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

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

Apply the Product Rule:

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

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

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

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

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

Popular Examples

derivative of 2xe^x+x^2e^x derivative of

2 x e^{x} + x^{2} e^{x}

derivative of 200x-(x^2)/(30)derivative of

200 x - \frac{x ^{2}}{30}

integral of (x^2-1)e^{x^3-3x-5}

\int (x^{2} - 1) e^{x^{3} - 3 x - 5} d x

tangent of f(x)=(x^2)/(x+4),\at x=3 tangent of

f (x) = \frac{x ^{2}}{x + 4}, at x = 3

derivative of e^{5x^4}

\frac{d}{d x} (e^{5 x^{4}})

Frequently Asked Questions (FAQ)

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