What is the derivative of 5sin(t)cos(t) ?

The derivative of 5sin(t)cos(t) is 5cos(2t)

What is the first derivative of 5sin(t)cos(t) ?

The first derivative of 5sin(t)cos(t) is 5cos(2t)

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derivative of

5 sin (t) cos (t)

5 cos (2 t)

Solution steps

\frac{d}{d t} (5 sin (t) cos (t))

Take the constant out:

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

= 5 \frac{d}{d t} (sin (t) cos (t))

Apply the Product Rule:

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

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

= 5 (\frac{d}{d t} (sin (t)) cos (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)

= 5 (cos (t) cos (t) + (- sin (t)) sin (t))

Simplify

5 (cos (t) cos (t) + (- sin (t)) sin (t)) : 5 cos (2 t)

= 5 cos (2 t)

cos (x), sin (2 x), x = 0, x = \frac{π}{2}

ln (x) x

f (x) = x^{4} + 4 e^{x}, (0, 4)

\frac{d y}{d t} = - 2 (y - 4)

\int \frac{x ^{2} + 16}{x ^{4}} d x

What is the derivative of 5sin(t)cos(t) ?
The derivative of 5sin(t)cos(t) is 5cos(2t)
What is the first derivative of 5sin(t)cos(t) ?
The first derivative of 5sin(t)cos(t) is 5cos(2t)