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

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

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

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

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

3 x + 4

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

= 3 x + 4

f (x) = x^{2} - 3 x - 2, at x = 2

\frac{d}{d x} (- \frac{b}{x ^{2}})

\frac{d y}{d x} = \frac{cos ( 7 x )}{e ^{7 y}}, y (0) = 0

x \to 1 + lim (x^{2} - 2)

y^{^{''}} - 6 y + 13 y = 0

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