Question

(a) Suppose f and g are di?erentiable on an interval I and that f(x) − ((g(x))n = c for all

xεI (where nεNand cεR are constants). If g(x) ̸= 0 on I, then g′(x) = −f(x)((g(x))1−n.n

(b) If f is not di?erentiable at x0,then f is not continuous at x0.

(c) Suppose f and g are di?erentiable on an interval I and suppose that f′(x) = g′(x)on I.

Then f(x) = g(x) on I.

(d) The equation of the line tangent to y = f(x) at the point (a, f(a)) is given by y − f(a) =(f′(x))(x − a).

(e) Iff(0)=0,thenf′(0)=0.

Find the indicated derative

d^99/dx^99.e^2x

d^n/dx^n[1/1-x]

Answer 1

Please write question number 1 properly again.