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The circle can be written (x+3)²+(y+5)^2 = 41 and so has center (-3,-5).
The gradient through the center and the point (-8,-1) is;m = (-5+1)/(-3+8) = -4/5.
The tangent line is perpend...

The first thing you want to do is to get rid of the fractions,Multiplying everything by 6 will help you do this You must multiply every fraction by 6 and also everything you do to the left hand side...

This is a simple differentiation question where we just differentiate by taking the power of the x and bringing that in front as a constant and then taking 1 off the power. So for the first term, x^4, we ...

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) = ...