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Popular >

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

Solution

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

Solution

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

Popular Examples

derivative of y=sqrt(5-x)derivative of

y = 5 - x

derivative of sqrt(4x^5+9)derivative of

4 x^{5} + 9

integral of 1/((144+x^2)^{3/2)}

\int \frac{1}{( 144 + x ^{2} ) ^{\frac{3}{2}}} d x

integral of (5x+2)/(x^2-1)

\int \frac{5 x + 2}{x ^{2} - 1} d x

(dy)/(dx)=y(xy^7-1)

\frac{d y}{d x} = y (x y^{7} - 1)

Frequently Asked Questions (FAQ)

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