What is the derivative of 4-5sin(2x+pi/4) ?

The derivative of 4-5sin(2x+pi/4) is -5sqrt(2)(cos(2x)-sin(2x))

What is the first derivative of 4-5sin(2x+pi/4) ?

The first derivative of 4-5sin(2x+pi/4) is -5sqrt(2)(cos(2x)-sin(2x))

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

- 52 (cos (2 x) - sin (2 x))

Solution steps

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

Simplify

4 - 5 sin (2 x + \frac{π}{4}) : 4 - \frac{5 ( 2 sin ( 2 x ) + 2 cos ( 2 x ) )}{2}

= \frac{d}{d x} (4 - \frac{5 ( 2 sin ( 2 x ) + 2 cos ( 2 x ) )}{2})

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (4) - \frac{d}{d x} (\frac{5 ( 2 sin ( 2 x ) + 2 cos ( 2 x ) )}{2})

\frac{d}{d x} (4) = 0

\frac{d}{d x} (\frac{5 ( 2 sin ( 2 x ) + 2 cos ( 2 x ) )}{2}) = 52 (cos (2 x) - sin (2 x))

= 0 - 52 (cos (2 x) - sin (2 x))

Simplify

= - 52 (cos (2 x) - sin (2 x))

t an g e n t f (x) = 2 x 1 - 3 x, at x = - 2

\int \frac{1}{x ^{2} - 3 x - 4} d x

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

\frac{\partial}{\partial x} (x + 9 y + 8 z)

\frac{d}{d x} (\frac{7}{3 x ^{7} - 12 x ^{6} + 2 x ^{2} - 9})

What is the derivative of 4-5sin(2x+pi/4) ?
The derivative of 4-5sin(2x+pi/4) is -5sqrt(2)(cos(2x)-sin(2x))
What is the first derivative of 4-5sin(2x+pi/4) ?
The first derivative of 4-5sin(2x+pi/4) is -5sqrt(2)(cos(2x)-sin(2x))