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Popular >

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

Solution

derivative of

y = x^{2} - x + 9

Solution

\frac{2 x - 1}{2 x ^{2} - x + 9}

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

Popular Examples

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\frac{d y}{( 5 - 3 y ) ^{2}} = \frac{d x}{2 ( 4 - x )}

laplacetransform e^{-0.75t}cos(4t)laplace transform

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\int \frac{1 - x ^{2}}{1 - x} d x

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\int \frac{t + 1}{3 t ^{2} + 6 t - 5} d t

Frequently Asked Questions (FAQ)

What is the derivative of y=sqrt(x^2-x+9) ?
The derivative of y=sqrt(x^2-x+9) is (2x-1)/(2sqrt(x^2-x+9))
What is the first derivative of y=sqrt(x^2-x+9) ?
The first derivative of y=sqrt(x^2-x+9) is (2x-1)/(2sqrt(x^2-x+9))