What is the derivative of pi*c*(cos((pix)/L))/(L) ?

The derivative of pi*c*(cos((pix)/L))/(L) is -(pi^2csin((pix)/L))/(L^2)

What is the first derivative of pi*c*(cos((pix)/L))/(L) ?

The first derivative of pi*c*(cos((pix)/L))/(L) is -(pi^2csin((pix)/L))/(L^2)

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derivative of

π \cdot c \cdot \frac{cos ( \frac{π x}{L} )}{L}

- \frac{π ^{2} c sin ( \frac{π x}{L} )}{L ^{2}}

Solution steps

\frac{d}{d x} (π c \frac{cos ( \frac{π x}{L} )}{L})

Treat

c, L

as a constant

Take the constant out:

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

= π c \frac{1}{L} \frac{d}{d x} (cos (\frac{π x}{L}))

Apply the chain rule:

- sin (\frac{π x}{L}) \frac{d}{d x} (\frac{π x}{L})

= - sin (\frac{π x}{L}) \frac{d}{d x} (\frac{π x}{L})

\frac{d}{d x} (\frac{π x}{L}) = \frac{π}{L}

= π c \frac{1}{L} (- sin (\frac{π x}{L}) \frac{π}{L})

Simplify

π c \frac{1}{L} (- sin (\frac{π x}{L}) \frac{π}{L}) : - \frac{π ^{2} c sin ( \frac{π x}{L} )}{L ^{2}}

= - \frac{π ^{2} c sin ( \frac{π x}{L} )}{L ^{2}}

\int 6 x^{2} sin (\frac{1}{2} x) d x

\frac{x ^{2} - 1}{x + 3}

e^{2 - t}

(t - 4)^{2}

\frac{\partial}{\partial y} (x^{3})

What is the derivative of pi*c*(cos((pix)/L))/(L) ?
The derivative of pi*c*(cos((pix)/L))/(L) is -(pi^2csin((pix)/L))/(L^2)
What is the first derivative of pi*c*(cos((pix)/L))/(L) ?
The first derivative of pi*c*(cos((pix)/L))/(L) is -(pi^2csin((pix)/L))/(L^2)