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Popular >

derivative of ln(x^2sqrt(1-x^2))

Solution

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

Solution

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

Graph

Popular Examples

derivative of ((x^2+1))/((x-1)^2)derivative of

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

(\partial)/(\partial x)(yx^3-xy^2+xy+13y)

\frac{\partial}{\partial x} (y x^{3} - x y^{2} + x y + 13 y)

integral of x/(x^2+y^2)

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

tangent of f(x)=9e^x,\at x=7 tangent of

f (x) = 9 e^{x}, at x = 7

integral from 1 to 12 of 1/(x-7)

\int_{1}^{12} \frac{1}{x - 7} d x

Frequently Asked Questions (FAQ)

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