What is the derivative of sqrt(6+\sqrt{5x)} ?

The derivative of sqrt(6+\sqrt{5x)} is (sqrt(5))/(4sqrt(x)\sqrt{6+\sqrt{5)sqrt(x)}}

What is the first derivative of sqrt(6+\sqrt{5x)} ?

The first derivative of sqrt(6+\sqrt{5x)} is (sqrt(5))/(4sqrt(x)\sqrt{6+\sqrt{5)sqrt(x)}}

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derivative of

6 + 5 x

\frac{5}{4 x 6 + 5 x}

Solution steps

\frac{d}{d x} (6 + 5 x)

Apply the chain rule:

\frac{1}{2 6 + 5 x} \frac{d}{d x} (6 + 5 x)

= \frac{1}{2 6 + 5 x} \frac{d}{d x} (6 + 5 x)

\frac{d}{d x} (6 + 5 x) = \frac{5}{2 x}

= \frac{1}{2 6 + 5 x} \cdot \frac{5}{2 x}

Simplify

\frac{1}{2 6 + 5 x} \cdot \frac{5}{2 x} : \frac{5}{4 x 6 + 5 x}

= \frac{5}{4 x 6 + 5 x}

What is the derivative of sqrt(6+\sqrt{5x)} ?
The derivative of sqrt(6+\sqrt{5x)} is (sqrt(5))/(4sqrt(x)\sqrt{6+\sqrt{5)sqrt(x)}}
What is the first derivative of sqrt(6+\sqrt{5x)} ?
The first derivative of sqrt(6+\sqrt{5x)} is (sqrt(5))/(4sqrt(x)\sqrt{6+\sqrt{5)sqrt(x)}}