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Popular >

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

Solution

derivative of

ln (x + x^{2} - 3)

Solution

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

Popular Examples

integral from 0 to 1 of 2pi(2-y)(8y^2)

\int_{0}^{1} 2 π (2 - y) (8 y^{2}) d y

(\partial)/(\partial x)(8x^6y^7-7x^5y^6)

\frac{\partial}{\partial x} (8 x^{6} y^{7} - 7 x^{5} y^{6})

integral of 6csc^2(x)

\int 6 csc^{2} (x) d x

derivative of 1/3 x^3 derivative of

\frac{1}{3} x^{3}

area y=-x^2+3x+1,y=-x+1 area

y = - x^{2} + 3 x + 1, y = - x + 1

Frequently Asked Questions (FAQ)

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