What is the derivative of 4sqrt(9x^2+5) ?

The derivative of 4sqrt(9x^2+5) is (36x)/(sqrt(9x^2+5))

What is the first derivative of 4sqrt(9x^2+5) ?

The first derivative of 4sqrt(9x^2+5) is (36x)/(sqrt(9x^2+5))

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

\frac{36 x}{9 x ^{2} + 5}

Solution steps

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the chain rule:

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

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

\frac{d}{d x} (9 x^{2} + 5) = 18 x

= 4 \cdot \frac{1}{2 9 x ^{2} + 5} \cdot 18 x

Simplify

4 \cdot \frac{1}{2 9 x ^{2} + 5} \cdot 18 x : \frac{36 x}{9 x ^{2} + 5}

= \frac{36 x}{9 x ^{2} + 5}

x^{2} + y^{2}

\frac{d y}{d x} = - \frac{( 2 x + ln ( y ) ) y}{x}

\int (3^{4} \cdot sin^{4} (x) - cos^{4} (x)) d x

\int \frac{3 e ^{x}}{e ^{2 x} + 4 e ^{x} + 4} d x

t \to \infty lim (e^{t})

What is the derivative of 4sqrt(9x^2+5) ?
The derivative of 4sqrt(9x^2+5) is (36x)/(sqrt(9x^2+5))
What is the first derivative of 4sqrt(9x^2+5) ?
The first derivative of 4sqrt(9x^2+5) is (36x)/(sqrt(9x^2+5))