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Popular >

derivative of sqrt((5+3x^5))

Solution

\frac{d}{d x} ((5 + 3 x)^{5})

Solution

\frac{15 ( 3 x + 5 ) ^{\frac{3}{2}}}{2}

Solution steps

\frac{d}{d x} ((5 + 3 x)^{5})

Apply the chain rule:

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

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

\frac{d}{d x} ((5 + 3 x)^{5}) = 15 (5 + 3 x)^{4}

= \frac{1}{2 ( 5 + 3 x ) ^{5}} \cdot 15 (5 + 3 x)^{4}

Simplify

\frac{1}{2 ( 5 + 3 x ) ^{5}} \cdot 15 (5 + 3 x)^{4} : \frac{15 ( 3 x + 5 ) ^{\frac{3}{2}}}{2}

= \frac{15 ( 3 x + 5 ) ^{\frac{3}{2}}}{2}

Popular Examples

limit as x approaches infinity of-3x+x

x \to \infty lim (- 3 x + x)

derivative of 4/5 x^{3/2}

\frac{d}{d x} (\frac{4}{5} x^{\frac{3}{2}})

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\int x^{2} 2 + x d x

derivative of ln((2x+1(x^2-2)))

\frac{d}{d x} (ln ((2 x + 1) (x^{2} - 2)))

derivative of 1/(x^2+3x+2)

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

Frequently Asked Questions (FAQ)

What is the derivative of sqrt((5+3x^5)) ?
The derivative of sqrt((5+3x^5)) is (15(3x+5)^{3/2})/2
What is the first derivative of sqrt((5+3x^5)) ?
The first derivative of sqrt((5+3x^5)) is (15(3x+5)^{3/2})/2