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

The derivative of sqrt(sin(x+cos(x))) is (cos(x)-sin(x))/(2sqrt(sin(x)+cos(x)))

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

The first derivative of sqrt(sin(x+cos(x))) is (cos(x)-sin(x))/(2sqrt(sin(x)+cos(x)))

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

\frac{cos ( x ) - sin ( x )}{2 sin ( x ) + cos ( x )}

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

\int_{0}^{2} x^{2} (x^{3} + 1)^{\frac{3}{2}} d x

3 x^{2}, x^{2} + 4, - 2, 2

ln (\frac{x}{x ^{2} + 6})

\int \frac{- 1}{x} d x

y (x + 7) + y^{^{'}} = 0

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