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Popular >

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

Solution

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

Solution

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}}

Graph

Popular Examples

(\partial)/(\partial y)(x^2+sin(xy))

\frac{\partial}{\partial y} (x^{2} + sin (x y))

integral from 0 to 1 of cos(x)

\int_{0}^{1} cos (x) d x

4y^{''}-y^'+2y=0,y(0)=2,y^'(0)=0

4 y^{^{''}} - y^{^{'}} + 2 y = 0, y (0) = 2, y^{^{'}} (0) = 0

limit as x approaches 3 of (3-x)/(|3-x|)

x \to 3 lim (\frac{3 - x}{∣ 3 - x ∣})

(\partial)/(\partial x)(3xe^{3xy})

\frac{\partial}{\partial x} (3 x e^{3 x y})

Frequently Asked Questions (FAQ)

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}