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2x - y = 74x + y = 23In this pair of simultaneous equations, we have two unknowns. We can solve them simultaneously using substitution or elimination, but I will go through the elimination method. I wish ...

Using quotient rule y = u/v - dy/dx = (v.du/dx - u.dv/dx)/v².u = cos(2x³) , a = 2x³. du/da = -sin(a), da/dx = 6x². From chain rule, we know that du/dx = du/da ....

This question requires the use of differentiation by product rule. First differentiate the first term, whilst keeping the second term the same, i.e. we get 2xln(3x). Secondly we keep the first term the sa...

Firstly, for the points of intersection we need to equate the two expressions for y. Since we know that they intersect at the origin, we can immediately cancel the x values and then solve the quadratic fo...

y = 4x²(x+3)⁵ . Use the product rule to find the first derivative of the curve, 8x(x+3)⁵ + 20x²(x+3)⁴ , and substitute x = -1 to find the gradient at...