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Popular >

derivative of 3sqrt(sin(x))

Solution

\frac{d}{d x} (3 sin (x))

Solution

\frac{3 cos ( x )}{2 sin ( x )}

Solution steps

\frac{d}{d x} (3 sin (x))

Take the constant out:

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

= 3 \frac{d}{d x} (sin (x))

Apply the chain rule:

\frac{1}{2 sin ( x )} \frac{d}{d x} (sin (x))

= \frac{1}{2 sin ( x )} \frac{d}{d x} (sin (x))

\frac{d}{d x} (sin (x)) = cos (x)

= 3 \cdot \frac{1}{2 sin ( x )} cos (x)

Simplify

3 \cdot \frac{1}{2 sin ( x )} cos (x) : \frac{3 cos ( x )}{2 sin ( x )}

= \frac{3 cos ( x )}{2 sin ( x )}

Popular Examples

f (y) = sin (y)

limit as x approaches 1 of e^{2x}

x \to 1 lim (e^{2 x})

area f(x)=-4x^2-4,g(x)=2x^2-9 area

f (x) = - 4 x^{2} - 4, g (x) = 2 x^{2} - 9

derivative of-3ln(cos(x/3))

\frac{d}{d x} (- 3 ln (cos (\frac{x}{3})))

limit as x approaches 0 of (ln(x))/3

x \to 0 lim (\frac{ln ( x )}{3})

Frequently Asked Questions (FAQ)

What is the derivative of 3sqrt(sin(x)) ?
The derivative of 3sqrt(sin(x)) is (3cos(x))/(2sqrt(sin(x)))
What is the first derivative of 3sqrt(sin(x)) ?
The first derivative of 3sqrt(sin(x)) is (3cos(x))/(2sqrt(sin(x)))