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Popular >

derivative of y=sin^2(4pit-5)

Solution

derivative of

y = sin^{2} (4 π t - 5)

Solution

8 π sin (4 π t - 5) cos (4 π t - 5)

Solution steps

\frac{d}{d t} (sin^{2} (4 π t - 5))

Apply the chain rule:

2 sin (4 π t - 5) \frac{d}{d t} (sin (4 π t - 5))

= 2 sin (4 π t - 5) \frac{d}{d t} (sin (4 π t - 5))

\frac{d}{d t} (sin (4 π t - 5)) = cos (4 π t - 5) \cdot 4 π

= 2 sin (4 π t - 5) cos (4 π t - 5) \cdot 4 π

Simplify

= 8 π sin (4 π t - 5) cos (4 π t - 5)

Popular Examples

derivative of x^pi

\frac{d}{d x} (x^{π})

derivative of sqrt(x^2-4)+sqrt(4-y^2)

\frac{d}{d x} (x^{2} - 4 + 4 - y^{2})

integral of x^2(x^3+1)^4

\int x^{2} (x^{3} + 1)^{4} d x

(\partial)/(\partial x)(x^2+y^2+48-xy-6x)

\frac{\partial}{\partial x} (x^{2} + y^{2} + 48 - x y - 6 x)

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

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

Frequently Asked Questions (FAQ)

What is the derivative of y=sin^2(4pit-5) ?
The derivative of y=sin^2(4pit-5) is 8pisin(4pit-5)cos(4pit-5)
What is the first derivative of y=sin^2(4pit-5) ?
The first derivative of y=sin^2(4pit-5) is 8pisin(4pit-5)cos(4pit-5)