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

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

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

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

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

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