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Popular >

derivative of sqrt(1+4sin(x))

Solution

\frac{d}{d x} (1 + 4 sin (x))

Solution

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

Solution steps

\frac{d}{d x} (1 + 4 sin (x))

Apply the chain rule:

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

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

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

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

Simplify

\frac{1}{2 1 + 4 sin ( x )} \cdot 4 cos (x) : \frac{2 cos ( x )}{1 + 4 sin ( x )}

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

Popular Examples

integral of-2ysqrt(-y^2+2)

\int - 2 y - y^{2} + 2 d y

tangent of f(x)=1-7x^2,(-2,-27)tangent of

f (x) = 1 - 7 x^{2}, (- 2, - 27)

(\partial)/(\partial x)(e^{xy}+x/y)

\frac{\partial}{\partial x} (e^{x y} + \frac{x}{y})

y^{''}+13y^'+42y=0

y^{^{''}} + 13 y^{^{'}} + 42 y = 0

y^{''}+4y=0,y(0)=0,y^'(0)=0

y^{^{''}} + 4 y = 0, y (0) = 0, y^{^{'}} (0) = 0

Frequently Asked Questions (FAQ)

What is the derivative of sqrt(1+4sin(x)) ?
The derivative of sqrt(1+4sin(x)) is (2cos(x))/(sqrt(1+4sin(x)))
What is the first derivative of sqrt(1+4sin(x)) ?
The first derivative of sqrt(1+4sin(x)) is (2cos(x))/(sqrt(1+4sin(x)))