What is the derivative of 1/3 cos((6pix-1/2)) ?

The derivative of 1/3 cos((6pix-1/2)) is -pisin((6pix-1)/2)

What is the first derivative of 1/3 cos((6pix-1/2)) ?

The first derivative of 1/3 cos((6pix-1/2)) is -pisin((6pix-1)/2)

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\frac{d}{d x} (\frac{1}{3} cos (\frac{6 π x - 1}{2}))

- π sin (\frac{6 π x - 1}{2})

Solution steps

\frac{d}{d x} (\frac{1}{3} cos (\frac{6 π x - 1}{2}))

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= \frac{1}{3} \frac{d}{d x} (cos (\frac{6 π x - 1}{2}))

Apply the chain rule:

- sin (\frac{6 π x - 1}{2}) \frac{d}{d x} (\frac{6 π x - 1}{2})

= - sin (\frac{6 π x - 1}{2}) \frac{d}{d x} (\frac{6 π x - 1}{2})

\frac{d}{d x} (\frac{6 π x - 1}{2}) = 3 π

= \frac{1}{3} (- sin (\frac{6 π x - 1}{2}) \cdot 3 π)

Simplify

\frac{1}{3} (- sin (\frac{6 π x - 1}{2}) \cdot 3 π) : - π sin (\frac{6 π x - 1}{2})

= - π sin (\frac{6 π x - 1}{2})

\int x^{7} sin (x^{8}) d x

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

y = 2 x^{2}

\int_{0}^{y + z} \frac{1}{( x + y + z ) ^{3}} d x

e^{x} (x - 1)

What is the derivative of 1/3 cos((6pix-1/2)) ?
The derivative of 1/3 cos((6pix-1/2)) is -pisin((6pix-1)/2)
What is the first derivative of 1/3 cos((6pix-1/2)) ?
The first derivative of 1/3 cos((6pix-1/2)) is -pisin((6pix-1)/2)