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First notice that f(x) = u/v. So f'(x) =[ v(u') - u(v')]/v² (the Quotient rule). After working it out, we find f'(x) = 6x/(x² + 5)² (the steps can be shown on the whiteboa...

Take u = 1+3x² , this gives that y = u^1/3 . By the chain rule we have that dy/dx = dy/du * du/dx. By differentiating y = u^1/3 with respect to u giv...

first of all we have to recognise the general form of the equation, similar to the equation of a line but we just have to add one more term due to the fact that it is a second degree equation: y=ax^2<...

For this you’ll want to use the integration by parts method. In this the form u use is:integral of udv = uv - integral of vduTherefore we can rewrite the integral as ln(x)*1 labelling 1 as dv and ln(x) as...

using pythagorus ( c^2 = b^2 + a^2) and plugging in 3 and 4 as a and b we get c^2 = 3^2 + 4^2 = 9 + 16 = 25. Taking the positive square root as sides can't be negative we get c = 5