What is the d/(dt)(asin(γt)+bcos(γt)) ?

The d/(dt)(asin(γt)+bcos(γt)) is acos(γt)γ-bγsin(γt)

What is the first d/(dt)(asin(γt)+bcos(γt)) ?

The first d/(dt)(asin(γt)+bcos(γt)) is acos(γt)γ-bγsin(γt)

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\frac{d}{d t} (a sin (γ t) + b cos (γ t))

a cos (γ t) γ - bγ sin (γ t)

Solution steps

\frac{d}{d t} (a sin (γ t) + b cos (γ t))

Treat

a, b, γ

as a constant

Apply the Sum/Difference Rule:

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

= \frac{d}{d t} (a sin (γ t)) + \frac{d}{d t} (b cos (γ t))

\frac{d}{d t} (a sin (γ t)) = a cos (γ t) γ

\frac{d}{d t} (b cos (γ t)) = - bγ sin (γ t)

= a cos (γ t) γ - bγ sin (γ t)

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

\int - 4 sin (- 2 t) d t

\int 3 t^{2} (t^{3} + 4)^{5} d t

\frac{1}{1 + \frac{1}{x}}, 0

\int_{- 1}^{1} (x - 1 - x^{2}) d x

What is the d/(dt)(asin(γt)+bcos(γt)) ?
The d/(dt)(asin(γt)+bcos(γt)) is acos(γt)γ-bγsin(γt)
What is the first d/(dt)(asin(γt)+bcos(γt)) ?
The first d/(dt)(asin(γt)+bcos(γt)) is acos(γt)γ-bγsin(γt)