with detailed solution handwritten neat and clean

5. Derivative Theorems: Using different theorems and processes for derivatives, find the derivative of the following functions in terms of x. a. f(x)= (using the limit definition) b. g(t) = (t-3) 12 c. h(x) = Vx+9xi- - 3 es d. A(x) = (ax5 - bx* + cdx3 + ex2 - fx - g)i, where, a,b, c.d,e,f,geZ* e. T(x) = VX-+2x-3 x2 f. H(x) = Vx2+2x+3 X2 (using logarithmic differentiation) g. yvx -n = xy + 2 (using implicit differentiation] h. y = = such that u = ex. i. 4xy2 + yx2 + 6 = 0. Solve for both - and dx dy 6. Higher-order Derivatives: Find all the higher order derivatives of the function. q(t) = 2+10-~18 + 317 - +5+ 3+3 - nt2 - 1 N