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Popular >

derivative of 5+1/2 sin(5pit)

Solution

derivative of

5 + \frac{1}{2} sin (5 π t)

Solution

\frac{5 π}{2} cos (5 π t)

Solution steps

\frac{d}{d t} (5 + \frac{1}{2} sin (5 π t))

Apply the Sum/Difference Rule:

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

= \frac{d}{d t} (5) + \frac{d}{d t} (\frac{1}{2} sin (5 π t))

\frac{d}{d t} (5) = 0

\frac{d}{d t} (\frac{1}{2} sin (5 π t)) = \frac{5 π}{2} cos (5 π t)

= 0 + \frac{5 π}{2} cos (5 π t)

Simplify

= \frac{5 π}{2} cos (5 π t)

Popular Examples

y^{''}-8y^'+20y=100x^2-91xe^x

y^{^{''}} - 8 y^{^{'}} + 20 y = 100 x^{2} - 91 x e^{x}

derivative of x^{-1/4}

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

derivative of (250/(1+4e^{-0.75x)})

\frac{d}{d x} (\frac{250}{1 + 4 e ^{- 0.75 x}})

integral of (-e^{4x})/(4x)

\int \frac{- e ^{4 x}}{4 x} d x

integral of 27x^2cos(3x)

\int 27 x^{2} cos (3 x) d x

Frequently Asked Questions (FAQ)

What is the derivative of 5+1/2 sin(5pit) ?
The derivative of 5+1/2 sin(5pit) is (5pi)/2 cos(5pit)
What is the first derivative of 5+1/2 sin(5pit) ?
The first derivative of 5+1/2 sin(5pit) is (5pi)/2 cos(5pit)