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)

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

- 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}

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)