What is the d/(dt)(cos(t)sin(t)) ?

The d/(dt)(cos(t)sin(t)) is cos(2t)

What is the first d/(dt)(cos(t)sin(t)) ?

The first d/(dt)(cos(t)sin(t)) is cos(2t)

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\frac{d}{d t} (cos (t) sin (t))

cos (2 t)

Solution steps

\frac{d}{d t} (cos (t) sin (t))

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = cos (t), g = sin (t)

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

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

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

= (- sin (t)) sin (t) + cos (t) cos (t)

Simplify

(- sin (t)) sin (t) + cos (t) cos (t) : cos (2 t)

= cos (2 t)

\frac{\partial}{\partial x} (\frac{x}{( x ^{2} + y ^{2} )})

\int 7 x (8 - x) d x

y^{2} = 4 + x, y^{2} + x = 2

f (x) = (1 + 2 x^{2})^{2} + 2 x^{3}

\int_{0}^{1} 1 + x^{3} d x

What is the d/(dt)(cos(t)sin(t)) ?
The d/(dt)(cos(t)sin(t)) is cos(2t)
What is the first d/(dt)(cos(t)sin(t)) ?
The first d/(dt)(cos(t)sin(t)) is cos(2t)