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When differentiating an equation (y) you find the equation of the gradient, called dy/dx. The rule for differentiating a power of x is given below:y=x^n dy/dx= nx^(n-1)Applying this rule to this question ...

The very first step in solving this problem is understanding that a stationary point is where the derivative of the curve, dy/dx (or in Newton’s notation y’), is equal to zero. This is because at stationa...

Quotient rule: d(u/v)/dx = [(du/dx)v-u(dv/dx)]/v^2
u = ln(3x)
v = e^4x
Find du/dx using chain rule:
u = ln(z) ==> du/dz = 1/z
z = 3x ==> dz/dx = 3
(du/dz)(dz/dx) = ...

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: ...