Use Leibniz' rule above to evaluate the following derivative: r 4 d (1 + at) 6 dt = 1 t Ensure you take note of which variable you are integrating and differentiating with respect to. For example, you may use Leibniz' rule to find that 2 d dt cos(x4) de =To wrap up the calculus lessons, we'll consider a few questions on Leibniz' rule. This is a theorem on the calculus of multivariate functions which describes the derivatives of integrals of bivariate functions when, unlike the fundamental theorem of calculus, we are differentiating and integrating with respect to different variables. Suppose a, b are both univariate functions (in c, say) with continuous derivatives over an interval [c, d). Suppose we also have a function f in two variables r and t such that both f and of are continuous in both variables over the region {(z, t) ER2 : I E [C, d), te [a(x), b(z)] Then, for all a E [c, d], we have the formula d pb(I) b(x) ( of Ja(z) f(z, t) dt = Ja(z) or (I, t)) dt +f(z, b(z) ) b' (x) - f(z, a(z)) a' (2). Note: Remember to write your answers using Matlab syntax. 2ct cos(x- ) sint For example, the polynomial would be written as 2 Inc 2*x*t*cos (x*2) *sin (t) / (2*log (x) )