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Popular >

derivative of x^{-3/4}+x^{3/4}

Solution

derivative of

x^{- \frac{3}{4}} + x^{\frac{3}{4}}

Solution

- \frac{3}{4 x ^{\frac{7}{4}}} + \frac{3}{4 x ^{\frac{1}{4}}}

Solution steps

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

Apply the Sum/Difference Rule:

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

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

\frac{d}{d x} (x^{- \frac{3}{4}}) = - \frac{3}{4 x ^{\frac{7}{4}}}

\frac{d}{d x} (x^{\frac{3}{4}}) = \frac{3}{4 x ^{\frac{1}{4}}}

= - \frac{3}{4 x ^{\frac{7}{4}}} + \frac{3}{4 x ^{\frac{1}{4}}}

Graph

Popular Examples

derivative of 2ln(2x+5)

\frac{d}{d x} (2 ln (2 x + 5))

derivative of x/(1+2x)

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

integral of x/(x^4+25)

\int \frac{x}{x ^{4} + 25} d x

integral of 5/(sqrt(x))

\int \frac{5}{x} d x

y^2+(x^2(dy)/(dx))=(xy)(dy)/(dx)

y^{2} + (x^{2} \frac{d y}{d x}) = (x y) \frac{d y}{d x}

Frequently Asked Questions (FAQ)

What is the derivative of x^{-3/4}+x^{3/4} ?
The derivative of x^{-3/4}+x^{3/4} is -3/(4x^{7/4)}+3/(4x^{1/4)}
What is the first derivative of x^{-3/4}+x^{3/4} ?
The first derivative of x^{-3/4}+x^{3/4} is -3/(4x^{7/4)}+3/(4x^{1/4)}