What is the derivative of 4sqrt(7x^2+9) ?

The derivative of 4sqrt(7x^2+9) is (28x)/(sqrt(7x^2+9))

What is the first derivative of 4sqrt(7x^2+9) ?

The first derivative of 4sqrt(7x^2+9) is (28x)/(sqrt(7x^2+9))

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\frac{d}{d x} (4 7 x^{2} + 9)

\frac{28 x}{7 x ^{2} + 9}

Solution steps

\frac{d}{d x} (4 7 x^{2} + 9)

Take the constant out:

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

= 4 \frac{d}{d x} (7 x^{2} + 9)

Apply the chain rule:

\frac{1}{2 7 x ^{2} + 9} \frac{d}{d x} (7 x^{2} + 9)

= \frac{1}{2 7 x ^{2} + 9} \frac{d}{d x} (7 x^{2} + 9)

\frac{d}{d x} (7 x^{2} + 9) = 14 x

= 4 \cdot \frac{1}{2 7 x ^{2} + 9} \cdot 14 x

Simplify

4 \cdot \frac{1}{2 7 x ^{2} + 9} \cdot 14 x : \frac{28 x}{7 x ^{2} + 9}

= \frac{28 x}{7 x ^{2} + 9}

What is the derivative of 4sqrt(7x^2+9) ?
The derivative of 4sqrt(7x^2+9) is (28x)/(sqrt(7x^2+9))
What is the first derivative of 4sqrt(7x^2+9) ?
The first derivative of 4sqrt(7x^2+9) is (28x)/(sqrt(7x^2+9))