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Popular >

derivative of 8(x+2^{3/2})

Solution

\frac{d}{d x} (8 (x + 2)^{\frac{3}{2}})

Solution

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

Solution steps

\frac{d}{d x} (8 (x + 2)^{\frac{3}{2}})

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= 8 \frac{d}{d x} ((x + 2)^{\frac{3}{2}})

Apply the chain rule:

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

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

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

= 8 \cdot \frac{3 ( x + 2 ) ^{\frac{1}{2}}}{2} \cdot 1

Simplify

8 \cdot \frac{3 ( x + 2 ) ^{\frac{1}{2}}}{2} \cdot 1 : 12 (x + 2)^{\frac{1}{2}}

= 12 (x + 2)^{\frac{1}{2}}

Popular Examples

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\frac{d}{d x} (- 2 x^{4} + 3 x^{3} - x^{2})

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\frac{d y}{d x}, 40 x^{\frac{1}{3}} y^{\frac{2}{3}} = 480

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

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

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\frac{d}{d x} (\frac{4 y ^{2} - x ^{4}}{4 x y})

Frequently Asked Questions (FAQ)

What is the derivative of 8(x+2^{3/2}) ?
The derivative of 8(x+2^{3/2}) is 12(x+2)^{1/2}
What is the first derivative of 8(x+2^{3/2}) ?
The first derivative of 8(x+2^{3/2}) is 12(x+2)^{1/2}