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When differentiating an expression of x and y we can use implicit differentiation when terms contain the y variable, recall that this is essentially differentiating the y term by y and then multiplying by...

x²>3(x+6)Firsty expand brackets --> x²>3x+18Then make one side = to 0 ---> x²-3x-18>0Solve the quadratic (x+3)(x-6)>0find the solutions when =0 x=-3 and ...

First, lets sketch a simple y=sin(x) graph between 0 and 2Pi radians.There are 4 different places a number could be put into this equation to affect the y=sin(x) graph.y=2sin(x) will stretch the graph to ...

PRODUCT RULETherefore dy/dx=(x^3)(1/2x)(2)+(ln2x)(3x^2)=x^2+3x^2ln2x

Take the log of both sidesln(y) = ln(2^x)This can be re-written as:ln(y) = ln(2)*xTake the exponent of both sidese^ln(y) = e^(ln(2)*x)Which gives:y = e^(ln(2)*x)Since ln(2) is a constant, apply the usual ...