Explain the steps and clearly write the proofs where I can clearly follow as I have trouble understanding the subject in school I want to learn how to do it while you're writing out the proofs

47 The Derivative of a Determinant of Functions. a Let A (t) = $11 (t) 12 (t) . Show A' (t) = pil (t) 912 (t) Q11 ( t) 912 (t) + 21 (t) P22 ( t ) 21 (t) 22 (t) 21 (t) 22 (t ) b Generalize to 3 x 3 matrices of functions and prove. Hint: For a 3 x 3 matrix A with rows A1, A2, and A3, DetA = Det( A1, A2, A3) = Al . A2 x A3 - Consider the rows of A as differentiable curves in R' and recall there is a pretty formula for the derivative of the triple scalar product of three differentiable curves. c. Prove for the n xn case: If A(t) = Det(; (t)); Isi