Home › TS EAPCET (Engineering) › Mathematics › Continuity and Differentiability › Find dy/dx for y = x^(sin x), x > 0.
Find dy/dx for y = x^(sin x), x > 0.
Ax^(sin x)(sin x/x + cos x log x)
Bx^(sin x)(1/x + cos x log x)
Cx^(sin x)(sin x/x - cos x log x)
Dx^(sin x)(cos x/x + sin x log x)
Answer & Solution
Correct answer: A. x^(sin x)(sin x/x + cos x log x)
log y = sin x log x, so y'/y = sin x/x + cos x log x.
Related questions
The identity x = e^(log x) holds only forThe function f(x) = 1/(x - 2) is discontinuous atThe greatest integer function [x] is discontinuous at which of these points?For x > 0, logarithmic differentiation shows that the derivative of x^x isIf x^2 + y^2 = 1, implicit differentiation gives dy/dx equal toLet f(x) = kx^2 for x <= 2 and f(x) = 3 for x > 2. For continuity at x = 2, the value of kA function equals (x^2 - 9)/(x - 3) for x not equal to 3 and has value k at x = 3. It is cTaking natural logs of y = [u(x)]^v(x) gives log y equal to