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Find the derivatives of the given functions.$$y=3 x+2 \cos (3 x-\pi)$$

$\frac{d y}{d x}=3-6 \sin (3 x-\pi)$

Calculus 1 / AB

Chapter 27

Differentiation of Transcendental Functions

Section 1

Derivatives of the sine and Cosine Functions

Derivatives

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All right. We want to find dy dx for the function Y equals three X plus to co sign three x minus pi to do so, we're gonna rely on different shortcuts that we picked up through single variable calculus, particularly those relating to trigger geometric functions. Co sign inside. So these rules are on left. Zero is GDX in Mexico's coast. Xdd Exco sex is negative sine X. And then rules one through three on the right are the powerful product rule and change respectively. For this particular problem, we're gonna rely on rule 01 and three to solve so why equals three experts to cosign directions. Pie is already in the most easily differentiable form so we can proceed straight to the derivative. Dy dx is three. This is by the power rule minus. To sign three, explain this Pie. This is my rule zero Times three, multiplying the derivative. What's inside of three X -9. Thus we have final solution. D Y E x is equal to three minus six sign of three X minus pi.

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The number 2 is also the smallest & first prime number (since every other even number is divisible by two).

If you write pi (to the first two decimal places of 3.14) backwards, in big, block letters it actually reads "PIE".

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