What is the derivative of (4x^3+6(sqrt(x)+8)) ?

The derivative of (4x^3+6(sqrt(x)+8)) is (14x^3+96x^2sqrt(x)+3)/(sqrt(x))

What is the first derivative of (4x^3+6(sqrt(x)+8)) ?

The first derivative of (4x^3+6(sqrt(x)+8)) is (14x^3+96x^2sqrt(x)+3)/(sqrt(x))

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\frac{d}{d x} ((4 x^{3} + 6) (x + 8))

\frac{14 x ^{3} + 96 x ^{2} x + 3}{x}

Solution steps

\frac{d}{d x} ((4 x^{3} + 6) (x + 8))

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = 4 x^{3} + 6, g = x + 8

= \frac{d}{d x} (4 x^{3} + 6) (x + 8) + \frac{d}{d x} (x + 8) (4 x^{3} + 6)

\frac{d}{d x} (4 x^{3} + 6) = 12 x^{2}

\frac{d}{d x} (x + 8) = \frac{1}{2 x}

= 12 x^{2} (x + 8) + \frac{1}{2 x} (4 x^{3} + 6)

Simplify

12 x^{2} (x + 8) + \frac{1}{2 x} (4 x^{3} + 6) : \frac{14 x ^{3} + 96 x ^{2} x + 3}{x}

= \frac{14 x ^{3} + 96 x ^{2} x + 3}{x}

x \to \infty lim (7 x^{2} + 8)

x \to 0 + lim (sin (x) \cdot ln (2 x))

\frac{d}{d t} (e^{- t} cos (2 t))

x^{^{''}} + 16 π^{2} x = 0

\int (2 x + 5)^{4} d x

What is the derivative of (4x^3+6(sqrt(x)+8)) ?
The derivative of (4x^3+6(sqrt(x)+8)) is (14x^3+96x^2sqrt(x)+3)/(sqrt(x))
What is the first derivative of (4x^3+6(sqrt(x)+8)) ?
The first derivative of (4x^3+6(sqrt(x)+8)) is (14x^3+96x^2sqrt(x)+3)/(sqrt(x))