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Popular >

derivative of y=sqrt(x^2+9)

Solution

derivative of

y = x^{2} + 9

Solution

\frac{x}{x ^{2} + 9}

Solution steps

\frac{d}{d x} (x^{2} + 9)

Apply the chain rule:

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

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

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

= \frac{1}{2 x ^{2} + 9} \cdot 2 x

Simplify

\frac{1}{2 x ^{2} + 9} \cdot 2 x : \frac{x}{x ^{2} + 9}

= \frac{x}{x ^{2} + 9}

Popular Examples

y^'+y/t =e^{t^2}

y^{^{'}} + \frac{y}{t} = e^{t^{2}}

(d^2y)/(dx^2)-2(dy)/(dx)+y=(e^x)/(1+x^2)

\frac{d ^{2} y}{d x ^{2}} - 2 \frac{d y}{d x} + y = \frac{e ^{x}}{1 + x ^{2}}

limit as n approaches infinity of {(1+2/n)^{4n}}

n \to \infty lim ({(1 + \frac{2}{n})^{4 n}})

derivative of y=x^2e^x-2xe^x+9e^x derivative of

y = x^{2} e^{x} - 2 x e^{x} + 9 e^{x}

(dy)/(dx)-2y=-1

\frac{d y}{d x} - 2 y = - 1

Frequently Asked Questions (FAQ)

What is the derivative of y=sqrt(x^2+9) ?
The derivative of y=sqrt(x^2+9) is x/(sqrt(x^2+9))
What is the first derivative of y=sqrt(x^2+9) ?
The first derivative of y=sqrt(x^2+9) is x/(sqrt(x^2+9))