Find frac{d y}{d x} at x=frac{pi}{4}, when y=3 sin x cos x+2 tan x.

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Step:1 ：Given the function (y = 3sin(x)cos(x) + 2tan(x))Step:2 ：We need to find the derivative of this function, (frac{d y}{d x})Step:3 ：Using the chain rule, the derivative of (sin(x)cos(x)) is (-3sin^2(x) + 3cos^2(x)) and the derivative of (tan(x)) is (2tan^2(x) + 2)Step:4 ：So, (frac{d y}{d x} = -3sin^2(x) + 3cos^2(x) + 2tan^2(x) + 2)Step:5 ：We then substitute (x = frac{pi}{4}) into the derivativeStep:6 ：Which gives us (frac{d y}{d x} = 4) at (x = frac{pi}{4})Step:7 ：Final Answer: (boxed{4})

Answer

Step: 1 ：Given the function (y = 3sin(x)cos(x) + 2tan(x))Step: 2 ：We need to find the derivative of this function, (frac{d y}{d x})Step: 3 ：Using the chain rule, the derivative of (sin(x)cos(x)) is (-3sin^2(x) + 3cos^2(x)) and the derivative of (tan(x)) is (2tan^2(x) + 2)Step: 4 ：So, (frac{d y}{d x} = -3sin^2(x) + 3cos^2(x) + 2tan^2(x) + 2)Step: 5 ：We then substitute (x = frac{pi}{4}) into the derivativeStep: 6 ：Which gives us (frac{d y}{d x} = 4) at (x = frac{pi}{4})Step: 7 ：Final Answer: (boxed{4})

Find $\frac{d y}{d x}$ at $x=\frac{\pi}{4}$, when $y=3 \sin x \cos x+2 \tan x$.

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