Find the derivative of the following functions: y = 5/csc(t) - csc(t)/5 y = -1/2 cot x - sqrt(2) cos x + 1/3 log(7x) tan 2θ y = 1/csc(3x) - 1/cot x + sqrt(2)/e^(-x) - 6^(2x) + 2π/p

Here's how to solve the problem: Step 1: Rewrite the function using trigonometric identities and exponent rules. Recall that (1)/((x)) = (x) and (1)/((x)) = (x). Also, (1)/(e^-x) = e^x. y = (3x) - (x) + sqrt(2)e^x - 6^2x + (2)/(A) Step 2: Differentiate each term with respect to x. We use the following differentiation rules: • (d)/(dx)((ax)) = a(ax) • (d)/(dx)((x)) = ^2(x) • (d)/(dx)(e^x) = e^x • (d)/(dx)(a^bx) = b · a^bx (a) • (d)/(dx)(C) = 0 for a constant C Differentiating each term: • (d)/(dx)((3x)) = 3(3x) • (d)/(dx)(-(x)) = -^2(x) • (d)/(dx)(sqrt(2)e^x) = sqrt(2)e^x • (d)/(dx)(-6^2x) = -(2 · 6^2x (6)) = -2 · 6^2x (6) • (d)/(dx)((2)/(A)) = 0 (assuming A is a constant) Step 3: Combine the derivatives to find (dy)/(dx). (dy)/(dx) = 3(3x) - ^2(x) + sqrt(2)e^x - 2 · 6^2x (6) + 0 (dy)/(dx) = 3(3x) - ^2(x) + sqrt(2)e^x - 2 · 6^2x (6) The final answer is 3(3x) - ^2(x) + sqrt(2)e^x - 2 · 6^2x (6). Send me the next one 📸