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

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

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

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

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

3 x + 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} : 3 x + 2

= 3 x + 2

x \to - 3 lim (- (\frac{1}{x ^{2} - 9}))

\int \frac{3 x ^{3} + 6 x ^{2} + 3}{3 x + 3} d x

x \to \infty lim (0.6 6^{x})

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

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