What is the derivative of g(t)=5(cos(pit))^2 ?

The derivative of g(t)=5(cos(pit))^2 is -10picos(pit)sin(pit)

What is the first derivative of g(t)=5(cos(pit))^2 ?

The first derivative of g(t)=5(cos(pit))^2 is -10picos(pit)sin(pit)

derivative of

g (t) = 5 (cos (π t))^{2}

- 10 π cos (π t) sin (π t)

Solution steps

\frac{d}{d t} (5 (cos (π t))^{2})

Take the constant out:

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

= 5 \frac{d}{d t} ((cos (π t))^{2})

Apply the chain rule:

2 cos (π t) \frac{d}{d t} (cos (π t))

= 2 cos (π t) \frac{d}{d t} (cos (π t))

\frac{d}{d t} (cos (π t)) = - sin (π t) π

= 5 \cdot 2 cos (π t) (- sin (π t) π)

Simplify

= - 10 π cos (π t) sin (π t)

\frac{d y}{d x} = 2 x - 1 + 2 x y - y

s l o p e (- 19.7, 10.5), (- 18.9, 3.4)

\frac{d}{d x} (cos (2 π x))

in v erse l a pl a ce t^{6} e^{8 t}

f (x) = 3 e^{2 x}

What is the derivative of g(t)=5(cos(pit))^2 ?
The derivative of g(t)=5(cos(pit))^2 is -10picos(pit)sin(pit)
What is the first derivative of g(t)=5(cos(pit))^2 ?
The first derivative of g(t)=5(cos(pit))^2 is -10picos(pit)sin(pit)