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Popular >

derivative of f(x)=sqrt(x)-\sqrt[3]{x}

Solution

derivative of

f (x) = x - 3 x

Solution

\frac{1}{2 x} - \frac{1}{3 x ^{\frac{2}{3}}}

Solution steps

\frac{d}{d x} (x - 3 x)

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (x) - \frac{d}{d x} (3 x)

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

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

= \frac{1}{2 x} - \frac{1}{3 x ^{\frac{2}{3}}}

Graph

Popular Examples

derivative of f(x)=x^2+x-9 derivative of

f (x) = x^{2} + x - 9

limit as x approaches 1/8 of 1/x+x^{-1}

x \to \frac{1}{8} lim (\frac{1}{x} + x^{- 1})

integral of 1/(t^2+9)

\int \frac{1}{t ^{2} + 9} d t

implicit (dy)/(dx),x^2+y^2=36 implicit derivative

\frac{d y}{d x}, x^{2} + y^{2} = 36

integral of (4x^3+x^2)(3x^4+x^3)^8

\int (4 x^{3} + x^{2}) (3 x^{4} + x^{3})^{8} d x

Frequently Asked Questions (FAQ)

What is the derivative of f(x)=sqrt(x)-\sqrt[3]{x} ?
The derivative of f(x)=sqrt(x)-\sqrt[3]{x} is 1/(2sqrt(x))-1/(3x^{2/3)}
What is the first derivative of f(x)=sqrt(x)-\sqrt[3]{x} ?
The first derivative of f(x)=sqrt(x)-\sqrt[3]{x} is 1/(2sqrt(x))-1/(3x^{2/3)}