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Popular >

derivative of (x^2+1/(x^2)^5)

Solution

\frac{d}{d x} ((x^{2} + \frac{1}{x ^{2}})^{5})

Solution

5 (x^{2} + \frac{1}{x ^{2}})^{4} (2 x - \frac{2}{x ^{3}})

Solution steps

\frac{d}{d x} ((x^{2} + \frac{1}{x ^{2}})^{5})

Apply the chain rule:

5 (x^{2} + \frac{1}{x ^{2}})^{4} \frac{d}{d x} (x^{2} + \frac{1}{x ^{2}})

= 5 (x^{2} + \frac{1}{x ^{2}})^{4} \frac{d}{d x} (x^{2} + \frac{1}{x ^{2}})

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

= 5 (x^{2} + \frac{1}{x ^{2}})^{4} (2 x - \frac{2}{x ^{3}})

Popular Examples

tangent of f(x)=3e^x+x,\at x=0 tangent of

f (x) = 3 e^{x} + x, at x = 0

derivative of y= 1/x+1/(x^2)+1/(x^3)derivative of

y = \frac{1}{x} + \frac{1}{x ^{2}} + \frac{1}{x ^{3}}

integral of-x/1

\int - \frac{x}{1} d x

y^{''}-3y^'+2y=e^{3x}(1+x)

y^{^{''}} - 3 y^{^{'}} + 2 y = e^{3 x} (1 + x)

derivative of y=4^x(2x^4)derivative of

y = 4^{x} (2 x^{4})

Frequently Asked Questions (FAQ)

What is the derivative of (x^2+1/(x^2)^5) ?
The derivative of (x^2+1/(x^2)^5) is 5(x^2+1/(x^2))^4(2x-2/(x^3))
What is the first derivative of (x^2+1/(x^2)^5) ?
The first derivative of (x^2+1/(x^2)^5) is 5(x^2+1/(x^2))^4(2x-2/(x^3))