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Popular >

derivative of 4sqrt(x)+8x^{3/8}

Solution

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

Solution

\frac{2}{x ^{\frac{1}{2}}} + \frac{3}{x ^{\frac{5}{8}}}

Solution steps

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

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (4 x) + \frac{d}{d x} (8 x^{\frac{3}{8}})

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

\frac{d}{d x} (8 x^{\frac{3}{8}}) = \frac{3}{x ^{\frac{5}{8}}}

= \frac{2}{x ^{\frac{1}{2}}} + \frac{3}{x ^{\frac{5}{8}}}

Popular Examples

derivative of sqrt(((x^2-4^3)/(36)))

\frac{d}{d x} \frac{( x ^{2} - 4 ) ^{3}}{36}

limit as x approaches 1+of 1/(x^3)

x \to 1 + lim (\frac{1}{x ^{3}})

slope ofintercept (-5,-1),(0,3)slope intercept

(- 5, - 1), (0, 3)

(dy)/(dx)=(y+1)/(x^3)

\frac{d y}{d x} = \frac{y + 1}{x ^{3}}

sum from n=1 to infinity of ((3x)^n)/n

n = 1 \sum \infty \frac{( 3 x ) ^{n}}{n}

Frequently Asked Questions (FAQ)

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