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In order to solve this, the quadratic must be factorised. This means we're trying to get the equation into the form (x+a)(x+b)>0 where a and b are constants where a x b = -14 and a + b = -5. This turn...

The above function has several components with different rules on how to differentiate each of them. For each:(1) y = x²dy/dx = 2x This follows the general rule of differentiating polynomials: ...

the gradient of the curve = dy/dx
and dy/dx = (dy/dt)(dt/dx)
dy/dt = 8t + 1
dx/dt = 2 therefore dt/dx = 1/2
dy/dx as above = (8t + 1) * 1/2 = (8t + 1)/2
where t = 4, dy/dx = (8*4...

So the first step is to find the first differential of yTo do this we simply have to differentiate:so with C being our coefficient, n being the power that x is.we need to reduce the power of x by 1, whils...

It relates back to what we actually mean why we say dy/dx. Simply put, dy/dx means the rate of change of y with respect to the rate of change in x over a infinitely small space of time. Therefore, when we...