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Popular >

derivative of cos^2(x^3-ln(x^2-1))

Solution

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

Solution

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

Solution steps

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

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

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

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

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

Popular Examples

tangent of (x^3)/6-3x^2+((77x))/6-8,\at x=5 tangent of

\frac{x ^{3}}{6} - 3 x^{2} + \frac{( 77 x )}{6} - 8, at x = 5

derivative of t^3ln(t)derivative of

t^{3} ln (t)

(dy)/(dx)= y/(2+x^2)

\frac{d y}{d x} = \frac{y}{2 + x ^{2}}

limit as x approaches 0 of (e^x-2)/x

x \to 0 lim (\frac{e ^{x} - 2}{x})

limit as x approaches-8 of (8+x)/(8+x)

x \to - 8 lim (\frac{8 + x}{8 + x})

Frequently Asked Questions (FAQ)

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