What is the derivative of sqrt(x^3+x^5) ?

The derivative of sqrt(x^3+x^5) is (3x^2+5x^4)/(2sqrt(x^3+x^5))

What is the first derivative of sqrt(x^3+x^5) ?

The first derivative of sqrt(x^3+x^5) is (3x^2+5x^4)/(2sqrt(x^3+x^5))

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

\frac{3 x ^{2} + 5 x ^{4}}{2 x ^{3} + x ^{5}}

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

= \frac{3 x ^{2} + 5 x ^{4}}{2 x ^{3} + x ^{5}}

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