What is the derivative of sqrt(4cos(x)+12x) ?

The derivative of sqrt(4cos(x)+12x) is (-sin(x)+3)/(sqrt(cos(x)+3x))

What is the first derivative of sqrt(4cos(x)+12x) ?

The first derivative of sqrt(4cos(x)+12x) is (-sin(x)+3)/(sqrt(cos(x)+3x))

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derivative of

4 cos (x) + 12 x

\frac{- sin ( x ) + 3}{cos ( x ) + 3 x}

Solution steps

\frac{d}{d x} (4 cos (x) + 12 x)

Apply the chain rule:

\frac{1}{2 4 cos ( x ) + 12 x} \frac{d}{d x} (4 cos (x) + 12 x)

= \frac{1}{2 4 cos ( x ) + 12 x} \frac{d}{d x} (4 cos (x) + 12 x)

\frac{d}{d x} (4 cos (x) + 12 x) = - 4 sin (x) + 12

= \frac{1}{2 4 cos ( x ) + 12 x} (- 4 sin (x) + 12)

Simplify

\frac{1}{2 4 cos ( x ) + 12 x} (- 4 sin (x) + 12) : \frac{- sin ( x ) + 3}{cos ( x ) + 3 x}

= \frac{- sin ( x ) + 3}{cos ( x ) + 3 x}

What is the derivative of sqrt(4cos(x)+12x) ?
The derivative of sqrt(4cos(x)+12x) is (-sin(x)+3)/(sqrt(cos(x)+3x))
What is the first derivative of sqrt(4cos(x)+12x) ?
The first derivative of sqrt(4cos(x)+12x) is (-sin(x)+3)/(sqrt(cos(x)+3x))