What is the derivative of sqrt(4(x+2)^3) ?

The derivative of sqrt(4(x+2)^3) is (3(x+2)^{3/2})/(sqrt((x+2)^2))

What is the first derivative of sqrt(4(x+2)^3) ?

The first derivative of sqrt(4(x+2)^3) is (3(x+2)^{3/2})/(sqrt((x+2)^2))

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derivative of

4 (x + 2)^{3}

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

Solution steps

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

Apply the chain rule:

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

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

\frac{d}{d x} (4 (x + 2)^{3}) = 12 (x + 2)^{2}

= \frac{1}{2 4 ( x + 2 ) ^{3}} \cdot 12 (x + 2)^{2}

Simplify

\frac{1}{2 4 ( x + 2 ) ^{3}} \cdot 12 (x + 2)^{2} : \frac{3 ( x + 2 ) ^{\frac{3}{2}}}{( x + 2 ) ^{2}}

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

\int \frac{a}{s ^{2} - a ^{2}} d s

\frac{d}{d x} (I n x)

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

\int \frac{1}{u ^{2} + u} d u

\frac{( s + 2 )}{s ( s + 4 )}

What is the derivative of sqrt(4(x+2)^3) ?
The derivative of sqrt(4(x+2)^3) is (3(x+2)^{3/2})/(sqrt((x+2)^2))
What is the first derivative of sqrt(4(x+2)^3) ?
The first derivative of sqrt(4(x+2)^3) is (3(x+2)^{3/2})/(sqrt((x+2)^2))