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A derivative is a function that tells us the gradient of a curve at any point. Say you have a function like f(x)=x3+x2 and you want to know when the function is stationary, i.e. has ...
When integrating we add one to the power of x and divide the number in front of the x by the new power for each part of the function. So 2x^2 becomes 2/3 x^3, 4x becomes 4/2 x^2, 1 becomes 1/1 x^1. Then w...
d(sin3y)/dx= 3cos3y*(dy/dx)d(3ye^(-2x))/dx = -6ye^(-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 ...
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)/(l...
(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))/(12)))(-4.5x)^2] 16[1-18x+121.5x^2] 16-288x+1944x^2
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