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Derivative of 3x^2 is 3*(derivative of x^2) which is 3*(2x)=6x. Derivative of 5x is 5*(Derivative of x) which is 5*1=5 and derivative of (-1) is 0. Hence the answer is derivative of f(x) defined above is ...

Firstly, recognise the relevant equations. The two functions are y = mx and y = ln(x). As the straight line is a tangent, we know that at a certain point x₀, the functions and ...

No, and we may take a counterexample to see why. If y=x^5+5/3x^4, dy/dx=5x^4+20/3x^3, d2y/dx2=20x^3+20x*2=20x^2(x+1). Setting this to 0 will give us the candidates for a POI, but not all these numbers wil...

Using integration by parts let U=x therefore du=dx.Let dv=5e^x therefore v=5e^x.answer = x*5e^x - integral(5e^x) = (x-1)(5e^x)

Using chain and product rule.dy/dx=(20x^3)cos(2x) - (10x^4)sin(2x)