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Popular >

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

Solution

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

Solution

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}}

Popular Examples

integral from-2 to 1 of (8x^3-3x^2)

\int_{- 2}^{1} (8 x^{3} - 3 x^{2}) d x

(dy)/(dx)=3xe^y

\frac{d y}{d x} = 3 x e^{y}

derivative of-1/2 cos(x)

\frac{d}{d x} (- \frac{1}{2} cos (x))

tangent of (7-6x)^{1/2},\at x=-1 tangent of

(7 - 6 x)^{\frac{1}{2}}, at x = - 1

integral from 1 to 2 of 1/(x^3)

\int_{1}^{2} \frac{1}{x ^{3}} d x

Frequently Asked Questions (FAQ)

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}