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

The derivative of x^2sqrt(x^3+a^3) is (7x^4+4a^3x)/(2sqrt(x^3+a^3))

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

The first derivative of x^2sqrt(x^3+a^3) is (7x^4+4a^3x)/(2sqrt(x^3+a^3))

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

\frac{7 x ^{4} + 4 a ^{3} x}{2 x ^{3} + a ^{3}}

Solution steps

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

Apply the Product Rule:

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

f = x^{2}, g = x^{3} + a^{3}

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

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

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

= 2 x x^{3} + a^{3} + \frac{3 x ^{2}}{2 x ^{3} + a ^{3}} x^{2}

Simplify

2 x x^{3} + a^{3} + \frac{3 x ^{2}}{2 x ^{3} + a ^{3}} x^{2} : \frac{7 x ^{4} + 4 a ^{3} x}{2 x ^{3} + a ^{3}}

= \frac{7 x ^{4} + 4 a ^{3} x}{2 x ^{3} + a ^{3}}

\int \frac{3 x ^{3} + 3 x + 2}{x ^{3} + x} d x

f (x) = \frac{1}{x ^{4}}, at x = 3

\frac{\partial}{\partial z} (x e^{z})

\int x^{2} + 3 x - 1000000 d x

\frac{1}{x + 9}

What is the derivative of x^2sqrt(x^3+a^3) ?
The derivative of x^2sqrt(x^3+a^3) is (7x^4+4a^3x)/(2sqrt(x^3+a^3))
What is the first derivative of x^2sqrt(x^3+a^3) ?
The first derivative of x^2sqrt(x^3+a^3) is (7x^4+4a^3x)/(2sqrt(x^3+a^3))