What is the derivative of 4cos(10^6t-y) ?

The derivative of 4cos(10^6t-y) is -4000000sin(1000000t-y)

What is the first derivative of 4cos(10^6t-y) ?

The first derivative of 4cos(10^6t-y) is -4000000sin(1000000t-y)

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derivative of

4 cos (1 0^{6} t - y)

- 4000000 sin (1000000 t - y)

Solution steps

\frac{d}{d t} (4 cos (1 0^{6} t - y))

Simplify

4 cos (1 0^{6} t - y) : 4 cos (1000000 t - y)

= \frac{d}{d t} (4 cos (1000000 t - y))

Treat

y

as a constant

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= 4 \frac{d}{d t} (cos (1000000 t - y))

Apply the chain rule:

- sin (1000000 t - y) \frac{d}{d t} (1000000 t - y)

= - sin (1000000 t - y) \frac{d}{d t} (1000000 t - y)

\frac{d}{d t} (1000000 t - y) = 1000000

= 4 (- sin (1000000 t - y) \cdot 1000000)

Simplify

= - 4000000 sin (1000000 t - y)

What is the derivative of 4cos(10^6t-y) ?
The derivative of 4cos(10^6t-y) is -4000000sin(1000000t-y)
What is the first derivative of 4cos(10^6t-y) ?
The first derivative of 4cos(10^6t-y) is -4000000sin(1000000t-y)