What is the derivative of f(x)=8sqrt(x^3+7x) ?

The derivative of f(x)=8sqrt(x^3+7x) is (4(3x^2+7))/(sqrt(x^3+7x))

What is the first derivative of f(x)=8sqrt(x^3+7x) ?

The first derivative of f(x)=8sqrt(x^3+7x) is (4(3x^2+7))/(sqrt(x^3+7x))

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derivative of

f (x) = 8 x^{3} + 7 x

\frac{4 ( 3 x ^{2} + 7 )}{x ^{3} + 7 x}

Solution steps

\frac{d}{d x} (8 x^{3} + 7 x)

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= 8 \frac{d}{d x} (x^{3} + 7 x)

Apply the chain rule:

\frac{1}{2 x ^{3} + 7 x} \frac{d}{d x} (x^{3} + 7 x)

= \frac{1}{2 x ^{3} + 7 x} \frac{d}{d x} (x^{3} + 7 x)

\frac{d}{d x} (x^{3} + 7 x) = 3 x^{2} + 7

= 8 \cdot \frac{1}{2 x ^{3} + 7 x} (3 x^{2} + 7)

Simplify

8 \cdot \frac{1}{2 x ^{3} + 7 x} (3 x^{2} + 7) : \frac{4 ( 3 x ^{2} + 7 )}{x ^{3} + 7 x}

= \frac{4 ( 3 x ^{2} + 7 )}{x ^{3} + 7 x}

\int (x^{2} - 6 x) d x

x \to 0 lim (h (x))

\frac{d}{d x} (e^{5 x})

\int \frac{1}{1 - 6 x ^{2}} d x

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

What is the derivative of f(x)=8sqrt(x^3+7x) ?
The derivative of f(x)=8sqrt(x^3+7x) is (4(3x^2+7))/(sqrt(x^3+7x))
What is the first derivative of f(x)=8sqrt(x^3+7x) ?
The first derivative of f(x)=8sqrt(x^3+7x) is (4(3x^2+7))/(sqrt(x^3+7x))