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

The derivative of sqrt(x^3+3x^2) is (3(x+2))/(2sqrt(x+3))

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

The first derivative of sqrt(x^3+3x^2) is (3(x+2))/(2sqrt(x+3))

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

\frac{3 ( x + 2 )}{2 x + 3}

Solution steps

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

Apply the chain rule:

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

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

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

= \frac{1}{2 x ^{3} + 3 x ^{2}} (3 x^{2} + 6 x)

Simplify

\frac{1}{2 x ^{3} + 3 x ^{2}} (3 x^{2} + 6 x) : \frac{3 ( x + 2 )}{2 x + 3}

= \frac{3 ( x + 2 )}{2 x + 3}

\int_{0}^{1} (x^{e} + e^{x}) d x

x^{10} h (x)

f (x) = sec^{2} (x) - 1

\int - 16 x^{2} d x

\int t^{2} sin (t^{3}) d t

What is the derivative of sqrt(x^3+3x^2) ?
The derivative of sqrt(x^3+3x^2) is (3(x+2))/(2sqrt(x+3))
What is the first derivative of sqrt(x^3+3x^2) ?
The first derivative of sqrt(x^3+3x^2) is (3(x+2))/(2sqrt(x+3))