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Popular >

d/(da)(sin^2(a)cos^2(a))

Solution

\frac{d}{d a} (sin^{2} (a) cos^{2} (a))

Solution

\frac{sin ( 4 a )}{2}

Solution steps

\frac{d}{d a} (sin^{2} (a) cos^{2} (a))

Apply the Product Rule:

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

f = sin^{2} (a), g = cos^{2} (a)

= \frac{d}{d a} (sin^{2} (a)) cos^{2} (a) + \frac{d}{d a} (cos^{2} (a)) sin^{2} (a)

\frac{d}{d a} (sin^{2} (a)) = sin (2 a)

\frac{d}{d a} (cos^{2} (a)) = - sin (2 a)

= sin (2 a) cos^{2} (a) + (- sin (2 a)) sin^{2} (a)

Simplify

sin (2 a) cos^{2} (a) + (- sin (2 a)) sin^{2} (a) : \frac{sin ( 4 a )}{2}

= \frac{sin ( 4 a )}{2}

Popular Examples

y^'+y= 1/(1+e^{2x)}

y^{^{'}} + y = \frac{1}{1 + e ^{2 x}}

derivative of (x^4+3x^2)(1-5x)derivative of

(x^{4} + 3 x^{2}) (1 - 5 x)

derivative of sqrt(2x)+1

\frac{d}{d x} (2 x + 1)

derivative of f(x)=(cos(x))/(x^7)derivative of

f (x) = \frac{cos ( x )}{x ^{7}}

integral of (3x^2+2)/(x^3+2x)

\int \frac{3 x ^{2} + 2}{x ^{3} + 2 x} d x

Frequently Asked Questions (FAQ)

What is the d/(da)(sin^2(a)cos^2(a)) ?
The d/(da)(sin^2(a)cos^2(a)) is (sin(4a))/2
What is the first d/(da)(sin^2(a)cos^2(a)) ?
The first d/(da)(sin^2(a)cos^2(a)) is (sin(4a))/2