Top answers

A curve C is defined by the equation sin3y + 3y*e^(-2x) + 2x^2 = 5, find dy/dx

d(sin3y)/dx= 3cos3y*(dy/dx)d(3y e^(-2x))/dx = -6y e^(-2x) + 3(dy/dx) e^(-2x)d(2x^2)/dx = 4xd(5)/dx = 0so3cos3y (dy/dx) - 6y*e^(-2x) + 3(dy/dx) e^(-2x) + 4x = 0rearrange the equationdy/dx = (6y e^(-2x)-4x)/(3...
ZZ
Answered by Zhaohui Z. • Maths tutor
6084 Views

if a^x= b^y = (ab)^(xy) prove that x+y =1

ln(a^x) = ln(b^y) = ln((ab)^(xy)) xln(a) = xyln(ab) ln(a) = yln(ab) = y(ln(a) + ln(b)) y = ln(a)/(ln(a)+ln(b)) with same analysis for ln(b^y): ln(b) = x(ln(a) + ln(b))x = ln(b)/(ln(a)+ln(b)) x + y = (ln(a) +...
SC
Answered by Scott C. • Maths tutor
6210 Views

Find the first 3 terms, in ascending powers of x, of the binomial expansion of (2 – 9x)^4 giving each term in its simplest form.

(2-9x)^4 [2(1-4.5x)]^4 (2^4)(1-4.5x)^4 Using the binomial expansion formula 16[1+(4*(-4.5x))+(((4*(4-1))/(1 2))) (-4.5x)^2] 16[1-18x+121.5x^2] 16-288x+1944x^2
LJ
Answered by Lauren J. • Maths tutor
8453 Views

How to find gradient of functions

To find the gradient of a function, that has constant gradient you pick any two points. You label both the x and y co-ordinates of these two points.Then you subtract the y co-ordinates of these two points. Y...
SH
Answered by Sinan H. • Maths tutor
4358 Views

Integrate the function f(x) where f(x)= x^2 +sin(x) + sin^2(x)

Answer: Integral= x 3 /3+ x/2 - cos(x) -1/4 sin(2x) + C Using the general rule that integrating x n results in x (n+1) /(n+1), x 2 integrates to x 3 /3.sin(x) is integrated to -cos(x)To integrate sin 2 (x), ...
CH
Answered by Charlie H. • Maths tutor
4945 Views