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Popular >

derivative of sqrt(x^2+2x-3)

Solution

\frac{d}{d x} (x^{2} + 2 x - 3)

Solution

\frac{x + 1}{x ^{2} + 2 x - 3}

Solution steps

\frac{d}{d x} (x^{2} + 2 x - 3)

Apply the chain rule:

\frac{1}{2 x ^{2} + 2 x - 3} \frac{d}{d x} (x^{2} + 2 x - 3)

= \frac{1}{2 x ^{2} + 2 x - 3} \frac{d}{d x} (x^{2} + 2 x - 3)

\frac{d}{d x} (x^{2} + 2 x - 3) = 2 x + 2

= \frac{1}{2 x ^{2} + 2 x - 3} (2 x + 2)

Simplify

\frac{1}{2 x ^{2} + 2 x - 3} (2 x + 2) : \frac{x + 1}{x ^{2} + 2 x - 3}

= \frac{x + 1}{x ^{2} + 2 x - 3}

Popular Examples

integral of (arctan(9x))/(1+81x^2)

\int \frac{arctan ( 9 x )}{1 + 81 x ^{2}} d x

integral of (300)/(x^2sqrt(100-x^2))

\int \frac{300}{x ^{2} 100 - x ^{2}} d x

(\partial)/(\partial x)(cos^5(x^6y^7))

\frac{\partial}{\partial x} (cos^{5} (x^{6} y^{7}))

derivative of y=10(3x+1)(1-5x)derivative of

y = 10 (3 x + 1) (1 - 5 x)

integral of arccot(3y)

\int arccot (3 y) d y

Frequently Asked Questions (FAQ)

What is the derivative of sqrt(x^2+2x-3) ?
The derivative of sqrt(x^2+2x-3) is (x+1)/(sqrt(x^2+2x-3))
What is the first derivative of sqrt(x^2+2x-3) ?
The first derivative of sqrt(x^2+2x-3) is (x+1)/(sqrt(x^2+2x-3))