What is the derivative of f(x)=sqrt(3+5sin(x)) ?

The derivative of f(x)=sqrt(3+5sin(x)) is (5cos(x))/(2sqrt(3+5sin(x)))

What is the first derivative of f(x)=sqrt(3+5sin(x)) ?

The first derivative of f(x)=sqrt(3+5sin(x)) is (5cos(x))/(2sqrt(3+5sin(x)))

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derivative of

f (x) = 3 + 5 sin (x)

\frac{5 cos ( x )}{2 3 + 5 sin ( x )}

Solution steps

\frac{d}{d x} (3 + 5 sin (x))

Apply the chain rule:

\frac{1}{2 3 + 5 sin ( x )} \frac{d}{d x} (3 + 5 sin (x))

= \frac{1}{2 3 + 5 sin ( x )} \frac{d}{d x} (3 + 5 sin (x))

\frac{d}{d x} (3 + 5 sin (x)) = 5 cos (x)

= \frac{1}{2 3 + 5 sin ( x )} \cdot 5 cos (x)

Simplify

\frac{1}{2 3 + 5 sin ( x )} \cdot 5 cos (x) : \frac{5 cos ( x )}{2 3 + 5 sin ( x )}

= \frac{5 cos ( x )}{2 3 + 5 sin ( x )}

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What is the derivative of f(x)=sqrt(3+5sin(x)) ?
The derivative of f(x)=sqrt(3+5sin(x)) is (5cos(x))/(2sqrt(3+5sin(x)))
What is the first derivative of f(x)=sqrt(3+5sin(x)) ?
The first derivative of f(x)=sqrt(3+5sin(x)) is (5cos(x))/(2sqrt(3+5sin(x)))