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This comes up in C4 in A level maths and differentiating it could come up in C3. You can write a^x as exp(ln(a^x))=exp(xln(a)) then differentiating this, you get ln(a)exp(xln(a))=ln(a)a^x. By differen...
Prove by contradiction: Assume negation to be true i.e. √2 is rational Then √2 can be written in the form a/b where a and b are integers with no common factor (the fraction cannot be simplified) => a/b...
Differentiate y to get: dy/dx = 7-3x^2 , dy/dx = 0 , therefore x=(+/-)sqrt(7/3) d^2y/dx^2 = 6x , substitute x values in to y=7x-x^3 and d^2y/dx^2 to find coordinates and the type of the stationary point.<...
The stationary points on a curve of the form y=f(x) are where dy/dx = 0. To find dy/dx, differentiate using the product rule: dy/dx = 7e^x(d/dx(cosx)) + cosx(d/dx(7e^x)) = -sinx(7e^x) + cosx(7e^x). Now se...
I like to separate problems into small steps that are easy to follow. In this example these would be: STEP 1: make y the subject (meaning only y on the Left hand side - LHS); 3y = -5x - 3. STEP 2: divide ...
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