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Popular >

derivative of f(x)=ln(6-x^2)

Solution

derivative of

f (x) = ln (6 - x^{2})

Solution

- \frac{2 x}{6 - x ^{2}}

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

= - \frac{2 x}{6 - x ^{2}}

Popular Examples

(\partial)/(\partial x)(xcos(y)-ysin(x))

\frac{\partial}{\partial x} (x cos (y) - y sin (x))

tangent of y=(2x)/(x^2+1),(-1,-1)tangent of

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

limit as x approaches 1 of ((5-5x))/(1-sqrt(x))

x \to 1 lim (\frac{( 5 - 5 x )}{1 - x})

x(dy)/(dx)-y=0,y(a)=b

x \frac{d y}{d x} - y = 0, y (a) = b

y^{^{'}} + 2 x y = x

Frequently Asked Questions (FAQ)

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