What is (\partial)/(\partial x)(5+cos(0.5x-t)) ?

The answer to (\partial)/(\partial x)(5+cos(0.5x-t)) is -0.5sin(0.5x-t)

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(\partial)/(\partial x)(5+cos(0.5x-t))

\frac{\partial}{\partial x} (5 + cos (0.5 x - t))

- 0.5 sin (0.5 x - t)

Solution steps

\frac{\partial}{\partial x} (5 + cos (0.5 x - t))

Treat

t

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (5) + \frac{\partial}{\partial x} (cos (0.5 x - t))

\frac{\partial}{\partial x} (5) = 0

\frac{\partial}{\partial x} (cos (0.5 x - t)) = - sin (0.5 x - t) \cdot 0.5

= 0 - sin (0.5 x - t) \cdot 0.5

Simplify

= - 0.5 sin (0.5 x - t)

^{'} (\frac{1}{x ^{2}} - \frac{9}{x ^{4}}) (x + 5 x^{3})

\int 2 x (3 - x^{2})^{3} d x

\int \frac{x ^{5}}{x ^{6} + 6} d x

x \to - 1 lim (\frac{x ^{2}}{x + 1})

\frac{\partial}{\partial x} (ln (ln (2 x + 2 y)))

What is (\partial)/(\partial x)(5+cos(0.5x-t)) ?
The answer to (\partial)/(\partial x)(5+cos(0.5x-t)) is -0.5sin(0.5x-t)