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Popular >

derivative of f(t)=cos^2(pi/2-t)

Solution

derivative of

f (t) = cos^{2} (\frac{π}{2} - t)

Solution

sin (2 t)

Solution steps

\frac{d}{d t} (cos^{2} (\frac{π}{2} - t))

Simplify

cos^{2} (\frac{π}{2} - t) : sin^{2} (t)

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

Apply the chain rule:

2 sin (t) \frac{d}{d t} (sin (t))

= 2 sin (t) \frac{d}{d t} (sin (t))

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

= 2 sin (t) cos (t)

Use the Double Angle identity:

2 sin (x) cos (x) = sin (2 x)

= sin (2 t)

Popular Examples

derivative of 2x^2-5x+2

\frac{d}{d x} (2 x^{2} - 5 x + 2)

(x+2)^2y^'+3(x+2)y=4

(x + 2)^{2} y^{^{'}} + 3 (x + 2) y = 4

limit as x approaches 0+of 1+xe^{(2/x)}

x \to 0 + lim (1 + x e^{(\frac{2}{x})})

(dy)/(dx)=2y+y^5,y(0)=1

\frac{d y}{d x} = 2 y + y^{5}, y (0) = 1

integral of e^{6t}

\int e^{6 t} d t

Frequently Asked Questions (FAQ)

What is the derivative of f(t)=cos^2(pi/2-t) ?
The derivative of f(t)=cos^2(pi/2-t) is sin(2t)
What is the first derivative of f(t)=cos^2(pi/2-t) ?
The first derivative of f(t)=cos^2(pi/2-t) is sin(2t)