What is the derivative of y=sqrt(x^2+10x) ?

The derivative of y=sqrt(x^2+10x) is (x+5)/(sqrt(x^2+10x))

What is the first derivative of y=sqrt(x^2+10x) ?

The first derivative of y=sqrt(x^2+10x) is (x+5)/(sqrt(x^2+10x))

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derivative of

y = x^{2} + 10 x

\frac{x + 5}{x ^{2} + 10 x}

Solution steps

\frac{d}{d x} (x^{2} + 10 x)

Apply the chain rule:

\frac{1}{2 x ^{2} + 10 x} \frac{d}{d x} (x^{2} + 10 x)

= \frac{1}{2 x ^{2} + 10 x} \frac{d}{d x} (x^{2} + 10 x)

\frac{d}{d x} (x^{2} + 10 x) = 2 x + 10

= \frac{1}{2 x ^{2} + 10 x} (2 x + 10)

Simplify

\frac{1}{2 x ^{2} + 10 x} (2 x + 10) : \frac{x + 5}{x ^{2} + 10 x}

= \frac{x + 5}{x ^{2} + 10 x}

\frac{d y}{d x} = \frac{x ^{2} - 2 y}{x}, y (2) = 2

5 (2^{x})

\int (x + 2) (x + 3) d x

\int_{\frac{π}{6}}^{\frac{π}{2}} cot (x) d x

\int π x cos (n x) d x

What is the derivative of y=sqrt(x^2+10x) ?
The derivative of y=sqrt(x^2+10x) is (x+5)/(sqrt(x^2+10x))
What is the first derivative of y=sqrt(x^2+10x) ?
The first derivative of y=sqrt(x^2+10x) is (x+5)/(sqrt(x^2+10x))