What is the solution for (dy)/(dx)=2*cos(9pix-1) derivative of cos(9pix-1) ?

The solution for (dy)/(dx)=2*cos(9pix-1) derivative of cos(9pix-1) is y=-sin^2(9pix-1)+c_{1}

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(dy)/(dx)=2*cos(9pix-1) derivative of cos(9pix-1)

\frac{d y}{d x} = 2 \cdot cos (9 π x - 1) \frac{d}{d x} (cos (9 π x - 1))

y = - sin^{2} (9 π x - 1) + c_{1}

Solution steps

\frac{d y}{d x} = 2 \cdot cos (9 π x - 1) \frac{d}{d x} (cos (9 π x - 1))

Substitute

\frac{d y}{d x}

with

y^{'} (x)

y^{^{'}} (x) = 2 cos (9 π x - 1) (cos (9 π x - 1))^{^{'}}

Simplify

y^{'} (x) = 2 \cdot cos (9 π x - 1) (cos (9 π x - 1))^{'} : y^{'} (x) = - 18 π cos (9 π x - 1) sin (9 π x - 1)

f^{^{'}} (x) = g (x)

then

f (x) = \int g (x) d x

y = \int - 18 π cos (9 π x - 1) sin (9 π x - 1) d x

\int - 18 π cos (9 π x - 1) sin (9 π x - 1) d x = - sin^{2} (9 π x - 1) + c_{1}

y = - sin^{2} (9 π x - 1) + c_{1}

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What is the solution for (dy)/(dx)=2*cos(9pix-1) derivative of cos(9pix-1) ?
The solution for (dy)/(dx)=2*cos(9pix-1) derivative of cos(9pix-1) is y=-sin^2(9pix-1)+c_{1}