What is the derivative of 2cos(3x+2sin(10y)+3x-10y) ?

The derivative of 2cos(3x+2sin(10y)+3x-10y) is -6sin(3x)+20cos(10y)(dy)/(dx)+3-10(dy)/(dx)

What is the first derivative of 2cos(3x+2sin(10y)+3x-10y) ?

The first derivative of 2cos(3x+2sin(10y)+3x-10y) is -6sin(3x)+20cos(10y)(dy)/(dx)+3-10(dy)/(dx)

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\frac{d}{d x} (2 cos (3 x) + 2 sin (10 y) + 3 x - 10 y)

- 6 sin (3 x) + 20 cos (10 y) \frac{d y}{d x} + 3 - 10 \frac{d y}{d x}

Solution steps

\frac{d}{d x} (2 cos (3 x) + 2 sin (10 y) + 3 x - 10 y)

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (2 cos (3 x)) + \frac{d}{d x} (2 sin (10 y)) + \frac{d}{d x} (3 x) - \frac{d}{d x} (10 y)

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

\frac{d}{d x} (2 sin (10 y)) = 20 cos (10 y) \frac{d y}{d x}

\frac{d}{d x} (3 x) = 3

\frac{d}{d x} (10 y) = 10 \frac{d y}{d x}

= - 6 sin (3 x) + 20 cos (10 y) \frac{d y}{d x} + 3 - 10 \frac{d y}{d x}

y = 1 - 2 x - x^{2}

\frac{x ^{3} + 8}{3}

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

\frac{d}{d a} (sec^{2} (a) + cos^{2} (a))

\frac{2}{( x + 3 )}

What is the derivative of 2cos(3x+2sin(10y)+3x-10y) ?
The derivative of 2cos(3x+2sin(10y)+3x-10y) is -6sin(3x)+20cos(10y)(dy)/(dx)+3-10(dy)/(dx)
What is the first derivative of 2cos(3x+2sin(10y)+3x-10y) ?
The first derivative of 2cos(3x+2sin(10y)+3x-10y) is -6sin(3x)+20cos(10y)(dy)/(dx)+3-10(dy)/(dx)