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Popular >

derivative of y=8sqrt(x)+3x^{1/6}

Solution

derivative of

y = 8 x + 3 x^{\frac{1}{6}}

Solution

\frac{4}{x ^{\frac{1}{2}}} + \frac{1}{2 x ^{\frac{5}{6}}}

Solution steps

\frac{d}{d x} (8 x + 3 x^{\frac{1}{6}})

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (8 x) + \frac{d}{d x} (3 x^{\frac{1}{6}})

\frac{d}{d x} (8 x) = \frac{4}{x ^{\frac{1}{2}}}

\frac{d}{d x} (3 x^{\frac{1}{6}}) = \frac{1}{2 x ^{\frac{5}{6}}}

= \frac{4}{x ^{\frac{1}{2}}} + \frac{1}{2 x ^{\frac{5}{6}}}

Graph

Popular Examples

integral from 0 to 1 of pi(4-1/2 x)^2

\int_{0}^{1} π (4 - \frac{1}{2} x)^{2} d x

tangent of (2x-9)(x^2+6),\at x=3 tangent of

(2 x - 9) (x^{2} + 6), at x = 3

integral from 0 to 6 of 1

\int_{0}^{6} 1

integral of xsqrt(-7+8x-x^2)

\int x - 7 + 8 x - x^{2} d x

limit as x approaches 7 of 6x^{-1}

x \to 7 lim (6 x^{- 1})

Frequently Asked Questions (FAQ)

What is the derivative of y=8sqrt(x)+3x^{1/6} ?
The derivative of y=8sqrt(x)+3x^{1/6} is 4/(x^{1/2)}+1/(2x^{5/6)}
What is the first derivative of y=8sqrt(x)+3x^{1/6} ?
The first derivative of y=8sqrt(x)+3x^{1/6} is 4/(x^{1/2)}+1/(2x^{5/6)}