What is the derivative of sqrt(16(x+2^3)) ?

The derivative of sqrt(16(x+2^3)) is 6sqrt(x+2)

What is the first derivative of sqrt(16(x+2^3)) ?

The first derivative of sqrt(16(x+2^3)) is 6sqrt(x+2)

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\frac{d}{d x} (16 (x + 2)^{3})

6 x + 2

Solution steps

\frac{d}{d x} (16 (x + 2)^{3})

Apply the chain rule:

\frac{1}{2 16 ( x + 2 ) ^{3}} \frac{d}{d x} (16 (x + 2)^{3})

= \frac{1}{2 16 ( x + 2 ) ^{3}} \frac{d}{d x} (16 (x + 2)^{3})

\frac{d}{d x} (16 (x + 2)^{3}) = 48 (x + 2)^{2}

= \frac{1}{2 16 ( x + 2 ) ^{3}} \cdot 48 (x + 2)^{2}

Simplify

\frac{1}{2 16 ( x + 2 ) ^{3}} \cdot 48 (x + 2)^{2} : 6 x + 2

= 6 x + 2

What is the derivative of sqrt(16(x+2^3)) ?
The derivative of sqrt(16(x+2^3)) is 6sqrt(x+2)
What is the first derivative of sqrt(16(x+2^3)) ?
The first derivative of sqrt(16(x+2^3)) is 6sqrt(x+2)