How to differentiate y=(x^2+4x)^5
To differentiate y=(x2+4x)5 you need to use the chain rule. The chain rule uses the fact that dy/dx = dy/dt * dt/dx.
Here we create a new variable t, where t = x2+4x. Substituting this in the original equation gives y=t5.
Differentiating t=x2+4x with respect to x; dt/dx = 2x+4
Differentiating y=t5 with respect to t; dy/dt = 5t4
We can combine these two equations to find dy/dx, as the chain rule states dy/dx = dy/dt * dt/dx.
This gives dy/dx = 5t4*(2x+4)
Substituting in our value of t, gives the final answer dy/dx = 5(x2+4x)4(2x+4)
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The Curve, C, has equation: x^2 - 3xy - 4y^2 +64 =0 Find dy/dx in terms of x and y. [Taken from Edexcel C4 2015 Q6a]