What is the derivative of 1-sin(xcos(x)) ?

The derivative of 1-sin(xcos(x)) is -cos(2x)

What is the first derivative of 1-sin(xcos(x)) ?

The first derivative of 1-sin(xcos(x)) is -cos(2x)

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\frac{d}{d x} (1 - sin (x) cos (x))

- cos (2 x)

Solution steps

\frac{d}{d x} (1 - sin (x) cos (x))

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

\frac{d}{d x} (1) = 0

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

= 0 - cos (2 x)

Simplify

= - cos (2 x)

x \to \infty lim (x^{0})

\int t csc^{2} (\frac{3 t ^{2}}{2}) d t

n = 4 \sum \infty \frac{1}{n ^{2}}

\int sin (10 a) b xx d x

f (x) = \frac{6}{5 x + 2}, (- 1, - 2)

What is the derivative of 1-sin(xcos(x)) ?
The derivative of 1-sin(xcos(x)) is -cos(2x)
What is the first derivative of 1-sin(xcos(x)) ?
The first derivative of 1-sin(xcos(x)) is -cos(2x)