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First, we need to realise that we will be using the trigonometric identity sin(x)² + cos(x)² = 1
As our goal is to end up with an equation involving only sin, we will therefore ...

F'(x)=3x^2+4x-5
F(x)=(3/(2+1))(x^(2+1))+(4/(1+1)) (x^(1+1))-5(x^(0+1))

Answer: F(x)=x^3+2x^2-5x+c

This is a common question as we are often taught to differentiate by simply being told how to do the calculation, but not what it is we're really doing.
The concept
Diffe...

First of all let's start with a lttle explanationn of waht a polynomial is.

A polynomial is a function of x denoted f(x) which is defined as

f(x)=a₀+a₁...