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Popular >

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

Solution

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

Solution

\frac{6 x ln ^{2} ( x ^{2} - 3 )}{x ^{2} - 3}

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

3 ln^{2} (x^{2} - 3) \frac{2 x}{x ^{2} - 3} : \frac{6 x ln ^{2} ( x ^{2} - 3 )}{x ^{2} - 3}

= \frac{6 x ln ^{2} ( x ^{2} - 3 )}{x ^{2} - 3}

Popular Examples

implicit (dy)/(dx),x^2+y^2=4 implicit derivative

\frac{d y}{d x}, x^{2} + y^{2} = 4

derivative of y=log_{3}(8x-1)derivative of

y = lo g_{3} (8 x - 1)

(d^2)/(dx^2)(sqrt(1+x^2))

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

y^'+y/(6960)=0.0025862069

y^{^{'}} + \frac{y}{6960} = 0.0025862069

derivative of e^{(-x})

\frac{d}{d x} (e^{(- x)})

Frequently Asked Questions (FAQ)

What is the derivative of (ln(x^2-3)^3) ?
The derivative of (ln(x^2-3)^3) is (6xln^2(x^2-3))/(x^2-3)
What is the first derivative of (ln(x^2-3)^3) ?
The first derivative of (ln(x^2-3)^3) is (6xln^2(x^2-3))/(x^2-3)