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Popular >

derivative of y=ln(x+sqrt(x^2+6))

Solution

derivative of

y = ln (x + x^{2} + 6)

Solution

\frac{1}{x ^{2} + 6}

Solution steps

\frac{d}{d x} (ln (x + x^{2} + 6))

Apply the chain rule:

\frac{1}{x + x ^{2} + 6} \frac{d}{d x} (x + x^{2} + 6)

= \frac{1}{x + x ^{2} + 6} \frac{d}{d x} (x + x^{2} + 6)

\frac{d}{d x} (x + x^{2} + 6) = 1 + \frac{x}{x ^{2} + 6}

= \frac{1}{x + x ^{2} + 6} (1 + \frac{x}{x ^{2} + 6})

Simplify

\frac{1}{x + x ^{2} + 6} (1 + \frac{x}{x ^{2} + 6}) : \frac{1}{x ^{2} + 6}

= \frac{1}{x ^{2} + 6}

Popular Examples

taylor x^{1/4},16 taylor

x^{\frac{1}{4}}, 16

derivative of (ln(-2x^3+5x^2)/(-x))

\frac{d}{d x} (\frac{ln ( - 2 x ^{3} + 5 x ^{2} )}{- x})

f (x) = \frac{1}{1 + x}

limit as x approaches 1 of x^3-x+2

x \to 1 lim (x^{3} - x + 2)

2y^{''}+y^'-4y=0

2 y^{^{''}} + y^{^{'}} - 4 y = 0

Frequently Asked Questions (FAQ)

What is the derivative of y=ln(x+sqrt(x^2+6)) ?
The derivative of y=ln(x+sqrt(x^2+6)) is 1/(sqrt(x^2+6))
What is the first derivative of y=ln(x+sqrt(x^2+6)) ?
The first derivative of y=ln(x+sqrt(x^2+6)) is 1/(sqrt(x^2+6))