What is the derivative of (x^3+x^{3/2}) ?

The derivative of (x^3+x^{3/2}) is (3(3x^2+1)(x^3+x)^{1/2})/2

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

The first derivative of (x^3+x^{3/2}) is (3(3x^2+1)(x^3+x)^{1/2})/2

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Popular >

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

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

\frac{d}{d x} (2^{c o s (x)})

n = 0 \sum \infty 2^{3 - 2 n}

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

\frac{\partial}{\partial t} (2 s^{2} t^{2})

\int x^{2} 8 + x d x

What is the derivative of (x^3+x^{3/2}) ?
The derivative of (x^3+x^{3/2}) is (3(3x^2+1)(x^3+x)^{1/2})/2
What is the first derivative of (x^3+x^{3/2}) ?
The first derivative of (x^3+x^{3/2}) is (3(3x^2+1)(x^3+x)^{1/2})/2