What is the derivative of 3sqrt(x^2+8x) ?

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

What is the first derivative of 3sqrt(x^2+8x) ?

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

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\frac{d}{d x} (3 x^{2} + 8 x)

\frac{3 ( x + 4 )}{x ^{2} + 8 x}

Solution steps

\frac{d}{d x} (3 x^{2} + 8 x)

Take the constant out:

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

= 3 \frac{d}{d x} (x^{2} + 8 x)

Apply the chain rule:

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

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

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

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

Simplify

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

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

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