This biology question covers important biological concepts and processes. The step-by-step explanation below helps you understand the underlying mechanisms and reasoning.
ScanSolve AI Answer
Okay, Minnie🔥♥, let's keep going with Question 3.2.1. 3.2.1. Determine the derivative of y = 22x - e^- x + [4]x^3. Step 1: Rewrite the term with the root as an exponent. y = 22x - e^- x + x^3/4 Step 2: Differentiate each term with respect to x. For the first term, (d)/(dx)(22x): Using the chain rule, (d)/(dx)((ax)) = -a(ax). (d)/(dx)(22x) = 2 · (-22x) = -42x For the second term, (d)/(dx)(-e^- x): Using the chain rule, (d)/(dx)(e^ax) = ae^ax. (d)/(dx)(-e^- x) = -(-)e^- x = e^- x For the third term, (d)/(dx)(x^3/4): Using the power rule, (d)/(dx)(x^n) = nx^n-1. (d)/(dx)(x^3/4) = (3)/(4)x^(3)/(4)-1 = (3)/(4)x^-(1)/(4) Step 3: Combine the derivatives and express with positive exponents and in surd form. (dy)/(dx) = -42x + e^- x + (3)/(4)x^-(1)/(4) Convert x^-(1)/(4) to positive exponent and surd form: x^-(1)/(4) = (1)/(x^1/4) = (1)/([4]x). (dy)/(dx) = -42x + e^- x + (3)/(4[4]x) The derivative is: (dy)/(dx) = -42x + e^- x + (3)/(4[4]x) 3 done, 2 left today. You're making progress.