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Popular >

derivative of f(x)=4sin^2(0.5x)+1

Solution

derivative of

f (x) = 4 sin^{2} (0.5 x) + 1

Solution

4 sin (0.5 x) cos (0.5 x)

Solution steps

\frac{d}{d x} (4 sin^{2} (0.5 x) + 1)

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (4 sin^{2} (0.5 x)) + \frac{d}{d x} (1)

\frac{d}{d x} (4 sin^{2} (0.5 x)) = 4 sin (0.5 x) cos (0.5 x)

\frac{d}{d x} (1) = 0

= 4 sin (0.5 x) cos (0.5 x) + 0

Simplify

= 4 sin (0.5 x) cos (0.5 x)

Popular Examples

derivative of 10000(12+xe^{-0.05x})

\frac{d}{d x} (10000 (12 + x) e^{- 0.05 x})

limit as x approaches 1 of (4x-1)/(x-1)

x \to 1 lim (\frac{4 x - 1}{x - 1})

derivative of 1/5 (9x+8)^3 derivative of

\frac{1}{5} (9 x + 8)^{3}

tangent of f(x)=-4x^2-5x+2 tangent of

f (x) = - 4 x^{2} - 5 x + 2

limit as x approaches 4 of (x-2)/(x-4)

x \to 4 lim (\frac{x - 2}{x - 4})

Frequently Asked Questions (FAQ)

What is the derivative of f(x)=4sin^2(0.5x)+1 ?
The derivative of f(x)=4sin^2(0.5x)+1 is 4sin(0.5x)cos(0.5x)
What is the first derivative of f(x)=4sin^2(0.5x)+1 ?
The first derivative of f(x)=4sin^2(0.5x)+1 is 4sin(0.5x)cos(0.5x)