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Popular >

derivative of f(x)=4x^4-1/(4x^4)

Solution

derivative of

f (x) = 4 x^{4} - \frac{1}{4 x ^{4}}

Solution

16 x^{3} + \frac{1}{x ^{5}}

Solution steps

\frac{d}{d x} (4 x^{4} - \frac{1}{4 x ^{4}})

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (4 x^{4}) - \frac{d}{d x} (\frac{1}{4 x ^{4}})

\frac{d}{d x} (4 x^{4}) = 16 x^{3}

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

= 16 x^{3} - (- \frac{1}{x ^{5}})

Simplify

= 16 x^{3} + \frac{1}{x ^{5}}

Popular Examples

y^{''}+2y^'+y=-e^{-t}

y^{^{''}} + 2 y^{^{'}} + y = - e^{- t}

(\partial)/(\partial y)((x^3)/(x^2+y^2))

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

sum from n=1 to infinity of (-5x)^n

n = 1 \sum \infty (- 5 x)^{n}

integral of (x+4)(2x+1)

\int (x + 4) (2 x + 1) d x

(d^2)/(dx^2)(2x^2)

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

Frequently Asked Questions (FAQ)

What is the derivative of f(x)=4x^4-1/(4x^4) ?
The derivative of f(x)=4x^4-1/(4x^4) is 16x^3+1/(x^5)
What is the first derivative of f(x)=4x^4-1/(4x^4) ?
The first derivative of f(x)=4x^4-1/(4x^4) is 16x^3+1/(x^5)