What is the derivative of 5cos((pi/4 x)+pi/4) ?

The derivative of 5cos((pi/4 x)+pi/4) is -(5pisin((pix+pi)/4))/(4)

What is the first derivative of 5cos((pi/4 x)+pi/4) ?

The first derivative of 5cos((pi/4 x)+pi/4) is -(5pisin((pix+pi)/4))/(4)

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derivative of

5 cos ((\frac{π}{4} x) + \frac{π}{4})

- \frac{5 π sin ( \frac{π x + π}{4} )}{4}

Solution steps

\frac{d}{d x} (5 cos (\frac{π}{4} x + \frac{π}{4}))

Take the constant out:

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

= 5 \frac{d}{d x} (cos (\frac{π}{4} x + \frac{π}{4}))

Apply the chain rule:

- sin (\frac{π}{4} x + \frac{π}{4}) \frac{d}{d x} (\frac{π}{4} x + \frac{π}{4})

= - sin (\frac{π}{4} x + \frac{π}{4}) \frac{d}{d x} (\frac{π}{4} x + \frac{π}{4})

\frac{d}{d x} (\frac{π}{4} x + \frac{π}{4}) = \frac{π}{4}

= 5 (- sin (\frac{π}{4} x + \frac{π}{4}) \frac{π}{4})

Simplify

5 (- sin (\frac{π}{4} x + \frac{π}{4}) \frac{π}{4}) : - \frac{5 π sin ( \frac{π x + π}{4} )}{4}

= - \frac{5 π sin ( \frac{π x + π}{4} )}{4}

\frac{d}{d x} (3 x^{2} + y^{2} - 1)

\int_{0}^{1} (x - x^{4}) d x

y = 3 x, y = 7 x^{2}

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

\frac{d}{d x} (\frac{2 x}{5 - tan ( x )})

What is the derivative of 5cos((pi/4 x)+pi/4) ?
The derivative of 5cos((pi/4 x)+pi/4) is -(5pisin((pix+pi)/4))/(4)
What is the first derivative of 5cos((pi/4 x)+pi/4) ?
The first derivative of 5cos((pi/4 x)+pi/4) is -(5pisin((pix+pi)/4))/(4)