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Popular >

derivative of x^{-1/4}+x^{1/4}

Solution

derivative of

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

Solution

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

Solution steps

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

Apply the Sum/Difference Rule:

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

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

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

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

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

Popular Examples

tangent of f(x)=x^2-7,\at x=3 tangent of

f (x) = x^{2} - 7, at x = 3

area 2/x , 2/(x^2),4 area

\frac{2}{x}, \frac{2}{x ^{2}}, 4

derivative of 4arctan(sqrt(x))

\frac{d}{d x} (4 arctan (x))

(y-x)e^x+(1+e^x)y^'=0,y(1)=1

(y - x) e^{x} + (1 + e^{x}) y^{^{'}} = 0, y (1) = 1

implicit (dy)/(dx),50x^{1/3}y^{2/3}=600 implicit derivative

\frac{d y}{d x}, 50 x^{\frac{1}{3}} y^{\frac{2}{3}} = 600

Frequently Asked Questions (FAQ)

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