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

The derivative of (2x^2+1^{3/2}) is 6x(2x^2+1)^{1/2}

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

The first derivative of (2x^2+1^{3/2}) is 6x(2x^2+1)^{1/2}

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

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

Solution steps

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

Apply the chain rule:

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

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

\frac{d}{d x} (2 x^{2} + 1) = 4 x

= \frac{3 ( 2 x ^{2} + 1 ) ^{\frac{1}{2}}}{2} \cdot 4 x

Simplify

\frac{3 ( 2 x ^{2} + 1 ) ^{\frac{1}{2}}}{2} \cdot 4 x : 6 x (2 x^{2} + 1)^{\frac{1}{2}}

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

What is the derivative of (2x^2+1^{3/2}) ?
The derivative of (2x^2+1^{3/2}) is 6x(2x^2+1)^{1/2}
What is the first derivative of (2x^2+1^{3/2}) ?
The first derivative of (2x^2+1^{3/2}) is 6x(2x^2+1)^{1/2}