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Popular >

d/(dt)(5sin(t)cos(t))

Solution

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

Solution

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)

Popular Examples

integral of 8ln(\sqrt[3]{x})

integral from 1 to 2 of ln(3x)

\int_{1}^{2} ln (3 x) d x

integral of (sin(2x))/(33+cos^2(x))

\int \frac{sin ( 2 x )}{33 + cos ^{2} ( x )} d x

derivative of (x^2+3*sqrt(x))

\frac{d}{d x} ((x^{2} + 3) \cdot x)

derivative of x^2+36 derivative of

x^{2} + 36

Frequently Asked Questions (FAQ)

What is the d/(dt)(5sin(t)cos(t)) ?
The d/(dt)(5sin(t)cos(t)) is 5cos(2t)
What is the first d/(dt)(5sin(t)cos(t)) ?
The first d/(dt)(5sin(t)cos(t)) is 5cos(2t)