What is the derivative of x^2sqrt(x^3+1) ?

The derivative of x^2sqrt(x^3+1) is (7x^4+4x)/(2sqrt(x^3+1))

What is the first derivative of x^2sqrt(x^3+1) ?

The first derivative of x^2sqrt(x^3+1) is (7x^4+4x)/(2sqrt(x^3+1))

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derivative of

x^{2} x^{3} + 1

\frac{7 x ^{4} + 4 x}{2 x ^{3} + 1}

Solution steps

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

Apply the Product Rule:

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

f = x^{2}, g = x^{3} + 1

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

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

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

= 2 x x^{3} + 1 + \frac{3 x ^{2}}{2 x ^{3} + 1} x^{2}

Simplify

2 x x^{3} + 1 + \frac{3 x ^{2}}{2 x ^{3} + 1} x^{2} : \frac{7 x ^{4} + 4 x}{2 x ^{3} + 1}

= \frac{7 x ^{4} + 4 x}{2 x ^{3} + 1}

x \to 8 lim (x)

\int y^{3} (4 y^{2} - 25) d y

n = 4 \sum \infty \frac{1}{n}

\int 8 x^{3} (2 x^{4} + 4)^{4} d x

1 + (\frac{2}{5})^{\circ} x (\frac{2}{3})^{\circ} - 25

What is the derivative of x^2sqrt(x^3+1) ?
The derivative of x^2sqrt(x^3+1) is (7x^4+4x)/(2sqrt(x^3+1))
What is the first derivative of x^2sqrt(x^3+1) ?
The first derivative of x^2sqrt(x^3+1) is (7x^4+4x)/(2sqrt(x^3+1))