Class 12 Differentiation RD SHARMA Ex 116 Example 1, IF y= x^x^x^infinity, INFINITY TYPE , find dy/dxDifferentiation Formulas1 d\dx(sin x)=cosx2DERIVATIVE OF A TOWER OF EXPONENTS First, let us consider the derivative (with respect to x) of xˣ (which I will write as x^x) Let y = x^x Then y = e^ln(x)^x = e^ln(x)*x, where e is the base of natural logarithms Let u = ln(x)*x Then y = e Here we discuss How to solve Questions like y = x^x^x(infinity) in Differential Calculusyou can also watch our videosIntroduction of Graphs Rat
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Y=x^x^x^infinity derivative-Now on RHS apply product rule We get I/y*d (y)/dx=y/xlogx*d (y)/dx Bring d (y)/dx on one side Then take d (y)/dx common Finally take the remaining part on other side you will get= d (y)/dx=y^2/x (1ylogx) ankit singhKCET 19 Permutations and Combinations 3 If 2 x 2 y = 2 x y, then d y d x is KCET 4 Let P = a i j be a 3 × 3 matrix and let Q = b i j where b i j = 2 i j a i j for 1 ≤ i, j ≤ If the determinant of P is 2, then the determinant of the matrix Q is IIT JEE 12 Determinants 5
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