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12-92.
1. Find the derivative with respect to x of each of the following functions and simplify, factoring where possible. Homework Help ✎

1. f(x) = cos kx · sin kx

$\frac{1}{2}x^{-1/2}e^{\sqrt{x}}+\sqrt{x}e^{\sqrt{x}}\Big(\frac{1}{2}x^{-1/2}\Big)$

$\frac{1}{2}x^{-1/2}e^{\sqrt{x}}+\frac{1}{2}e^{\sqrt{x}}$

$-k\sin(kx)\sin(kx)+k\cos(kx)(\cos(kx)$

$k(\cos^2(x)-\sin^2(x))$

$\frac{3x^2\sqrt{\ln(1+x^2)}-x^3\cdot\frac{1}{2}(\ln(1+x^2))^{-1/2}\cdot\frac{2x}{1+x^2}}{\ln(1+x^2)}$

$\sec^2(p_0e^{-x^2})(-2xp_0e^{-x^2})$