What is the derivative of sqrt(4x^5+9) ?

The derivative of sqrt(4x^5+9) is (10x^4)/(sqrt(4x^5+9))

What is the first derivative of sqrt(4x^5+9) ?

The first derivative of sqrt(4x^5+9) is (10x^4)/(sqrt(4x^5+9))

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derivative of

4 x^{5} + 9

\frac{10 x ^{4}}{4 x ^{5} + 9}

Solution steps

\frac{d}{d x} (4 x^{5} + 9)

Apply the chain rule:

\frac{1}{2 4 x ^{5} + 9} \frac{d}{d x} (4 x^{5} + 9)

= \frac{1}{2 4 x ^{5} + 9} \frac{d}{d x} (4 x^{5} + 9)

\frac{d}{d x} (4 x^{5} + 9) = 20 x^{4}

= \frac{1}{2 4 x ^{5} + 9} \cdot 20 x^{4}

Simplify

\frac{1}{2 4 x ^{5} + 9} \cdot 20 x^{4} : \frac{10 x ^{4}}{4 x ^{5} + 9}

= \frac{10 x ^{4}}{4 x ^{5} + 9}

\int \frac{1}{( 144 + x ^{2} ) ^{\frac{3}{2}}} d x

\int \frac{5 x + 2}{x ^{2} - 1} d x

\frac{d y}{d x} = y (x y^{7} - 1)

\int sin^{3} (x co) s^{9} x d x

y = - 6 x^{2} + 5 x, (0, 0)

What is the derivative of sqrt(4x^5+9) ?
The derivative of sqrt(4x^5+9) is (10x^4)/(sqrt(4x^5+9))
What is the first derivative of sqrt(4x^5+9) ?
The first derivative of sqrt(4x^5+9) is (10x^4)/(sqrt(4x^5+9))