Answer to Question #178023 in Differential Equations for John

Question

y=sin3t find dy/dt

v=11sin4t - 5cos5t, find dv/dt

differentiate with respect to x

y=12e^5x

y=ln3x

Answer 1

Solution.

1)

$y=\sin{3t},\newline \frac{dy}{dt}=3\cos{3t}.$

2)

$v=11\sin{4t}-5\cos{5t},\newline \frac{dv}{dt}=44\cos{4t}+25\sin{5t}.$

3)

$y=12e^{5x},\newline \frac{dy}{dx}=60e^{5x}.$

4)

$y=\ln{3x},\newline \frac{dy}{dx}=\frac{3}{3x}=\frac{1}{x}.$