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Popular >

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

Solution

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

Solution

cos (2 t)

Solution steps

\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)

= \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)

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

Simplify

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

= cos (2 t)

Popular Examples

x(d^2y)/(dx^2)+(2(dy)/(dx))=0

x \frac{d ^{2} y}{d x ^{2}} + (2 \frac{d y}{d x}) = 0

y^'-4/x y=(y^3)/(x^3)

y^{^{'}} - \frac{4}{x} y = \frac{y ^{3}}{x ^{3}}

integral from 1 to 2 of x^4(ln(x))^2

\int_{1}^{2} x^{4} (ln (x))^{2} d x

derivative of-1/(4(x+1^{3/2)})

\frac{d}{d x} (- \frac{1}{4 ( x + 1 ) ^{\frac{3}{2}}})

integral from 1 to 2 of (3/x)

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

Frequently Asked Questions (FAQ)

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