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Popular >

derivative of ((x+3/(x-3))^4)

Solution

\frac{d}{d x} ((\frac{x + 3}{x - 3})^{4})

Solution

- \frac{24 ( x + 3 ) ^{3}}{( x - 3 ) ^{5}}

Solution steps

\frac{d}{d x} ((\frac{x + 3}{x - 3})^{4})

Apply the chain rule:

4 (\frac{x + 3}{x - 3})^{3} \frac{d}{d x} (\frac{x + 3}{x - 3})

= 4 (\frac{x + 3}{x - 3})^{3} \frac{d}{d x} (\frac{x + 3}{x - 3})

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

= 4 (\frac{x + 3}{x - 3})^{3} (- \frac{6}{( x - 3 ) ^{2}})

Simplify

4 (\frac{x + 3}{x - 3})^{3} (- \frac{6}{( x - 3 ) ^{2}}) : - \frac{24 ( x + 3 ) ^{3}}{( x - 3 ) ^{5}}

= - \frac{24 ( x + 3 ) ^{3}}{( x - 3 ) ^{5}}

Popular Examples

(\partial}{\partial x}(\frac{y-z)/x)

\frac{\partial}{\partial x} (\frac{y - z}{x})

integral from 0 to 1 of (sqrt(x)-x)^2

\int_{0}^{1} (x - x)^{2} d x

inverse oflaplace (s-4)/(s^2-8s+10)inverse laplace

\frac{s - 4}{s ^{2} - 8 s + 10}

derivative of t^{4/3}derivative of

t^{\frac{4}{3}}

tangent of f(x)=x^3-9x+4,(3,4)tangent of

f (x) = x^{3} - 9 x + 4, (3, 4)

Frequently Asked Questions (FAQ)

What is the derivative of ((x+3/(x-3))^4) ?
The derivative of ((x+3/(x-3))^4) is -(24(x+3)^3)/((x-3)^5)
What is the first derivative of ((x+3/(x-3))^4) ?
The first derivative of ((x+3/(x-3))^4) is -(24(x+3)^3)/((x-3)^5)