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Popular >

d/(da)(cos(a)*sin(a))

Solution

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

Solution

cos (2 a)

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

= (- sin (a)) sin (a) + cos (a) cos (a)

Simplify

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

= cos (2 a)

Graph

Popular Examples

integral of 6sin^2(xco)s^2x

\int 6 sin^{2} (x co) s^{2} x d x

area y=3x^3-x^2-10x,y=-x^2+2x area

y = 3 x^{3} - x^{2} - 10 x, y = - x^{2} + 2 x

derivative of 6/((x-1^2))

\frac{d}{d x} (\frac{6}{( x - 1 ) ^{2}})

tangent of f(x)=6cos(x)+3sin(2x)tangent of

f (x) = 6 cos (x) + 3 sin (2 x)

y^{''}-y^'-2y=0,y(0)=2,y^'(0)=2

y^{^{''}} - y^{^{'}} - 2 y = 0, y (0) = 2, y^{^{'}} (0) = 2

Frequently Asked Questions (FAQ)

What is the d/(da)(cos(a)*sin(a)) ?
The d/(da)(cos(a)*sin(a)) is cos(2a)
What is the first d/(da)(cos(a)*sin(a)) ?
The first d/(da)(cos(a)*sin(a)) is cos(2a)