What is (\partial)/(\partial x)(3+cos(0.4x-t)) ?

The answer to (\partial)/(\partial x)(3+cos(0.4x-t)) is -0.4sin(0.4x-t)

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(\partial)/(\partial x)(3+cos(0.4x-t))

\frac{\partial}{\partial x} (3 + cos (0.4 x - t))

- 0.4 sin (0.4 x - t)

Solution steps

\frac{\partial}{\partial x} (3 + cos (0.4 x - t))

Treat

t

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (3) + \frac{\partial}{\partial x} (cos (0.4 x - t))

\frac{\partial}{\partial x} (3) = 0

\frac{\partial}{\partial x} (cos (0.4 x - t)) = - sin (0.4 x - t) \cdot 0.4

= 0 - sin (0.4 x - t) \cdot 0.4

Simplify

= - 0.4 sin (0.4 x - t)

8 x^{2}

\frac{d y}{d x} = \frac{y}{x} + e^{- \frac{y}{x}}

y = 5 x^{2} - x^{3}

x \to 2 lim (\frac{x ^{2} + 4}{x - 2})

\frac{\partial}{\partial x} (3 x^{2} \cdot e^{x^{2} y})

What is (\partial)/(\partial x)(3+cos(0.4x-t)) ?
The answer to (\partial)/(\partial x)(3+cos(0.4x-t)) is -0.4sin(0.4x-t)