What is the derivative of sqrt(8x+\sqrt{9x)} ?

The derivative of sqrt(8x+\sqrt{9x)} is (16sqrt(x)+3)/(4sqrt(x)\sqrt{8x+3\sqrt{x)}}

What is the first derivative of sqrt(8x+\sqrt{9x)} ?

The first derivative of sqrt(8x+\sqrt{9x)} is (16sqrt(x)+3)/(4sqrt(x)\sqrt{8x+3\sqrt{x)}}

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derivative of

8 x + 9 x

\frac{16 x + 3}{4 x 8 x + 3 x}

Solution steps

\frac{d}{d x} (8 x + 9 x)

Apply the chain rule:

\frac{1}{2 8 x + 9 x} \frac{d}{d x} (8 x + 9 x)

= \frac{1}{2 8 x + 9 x} \frac{d}{d x} (8 x + 9 x)

\frac{d}{d x} (8 x + 9 x) = 8 + \frac{3}{2 x}

= \frac{1}{2 8 x + 9 x} (8 + \frac{3}{2 x})

Simplify

\frac{1}{2 8 x + 9 x} (8 + \frac{3}{2 x}) : \frac{16 x + 3}{4 x 8 x + 3 x}

= \frac{16 x + 3}{4 x 8 x + 3 x}

(1 + t)^{7}

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

\int_{1}^{6} x^{3} ln (4 x) d x

\frac{( s + 1 )}{( s + 2 ) ^{2}}

\int \frac{( ln ( x ) ) ^{22}}{x} d x

What is the derivative of sqrt(8x+\sqrt{9x)} ?
The derivative of sqrt(8x+\sqrt{9x)} is (16sqrt(x)+3)/(4sqrt(x)\sqrt{8x+3\sqrt{x)}}
What is the first derivative of sqrt(8x+\sqrt{9x)} ?
The first derivative of sqrt(8x+\sqrt{9x)} is (16sqrt(x)+3)/(4sqrt(x)\sqrt{8x+3\sqrt{x)}}