First Principles Example 2: x³ - Page 4
Questions
- If # y=acos(lnx)+bsin(lnx) # then show that? # x^2y^((n+2)) + (2n+1)xy^((n+1))+(n^2+1)y^((n)) = 0#
- What is the integral of this graph?
- What is the derivative of #x^n#?
- How do i integrate (9x²+6x+6)(x³+x²+2x)?
- How to solve #(d^2y) /dx^2 + a^2y = 0# ?
- How do I find the anti-derivative of #x^3sec^2(x) + 3x^2tan(x)#?
- What is the derivative of #y=(9e^(3x))/(5x-3)#?
- How can I find the derivative of #y=c^x# using first principles, where c is an integer?
- Show that #ln(1+x) < x-(x^2)/(2(1+x)), AA x>0#?
- How do you differentiate # y = ( 2x + 1) ^ { 5} ( x ^ { 3} - x + 1) ^ { 4}#?
- What is the first differential of #y = (2x+5)^3(6x-1)^5#?
- What is #int e^x dx# and #int xe^(x^2)dx#?
- How do you differentiate the following: #v=x^x#?
- If #x^m * y^n = (x + y)^(m + n)#. Then how will you prove that #dy/dx = y/x#??
- Find the laplacian of #ln(x^3+y^3+z^3-3xyz) #?
- What is the first differential of #f(x) = 2^xln(2x)#?
- How do you solve #x'(t)+x3 =0#?
- What is the general solution of the differential equation # xdy/dx=(x^3+xy^(2)+y^3)/(x^2+y^2) #?
- If #y=e^(mtan^-1x)#, check whether the equation #(1+x^2)y_(n+1)+(2nx-m)+n(n+1)y_(n-2) = 0# ?
- Prove that x+y=xy , if d^2y/dx^2=2 (y/x)^3?