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To find the gradient of the curve $y = x^n$ at the point $P(a,a^n)$, a chord joining Point P to Point $Q(a+h, (a+h)^n)$ on the same curve is drawn. By finding the gradient of the chord PQ, find the gradient of the tangent to the curve at $x=a$ as a limit when $h \rightarrow 0$

When I first looked at the question, my first thought was that the gradient of tangent = gradient of chord.

However, I fail to find the gradient of chord using First Principle. What is the working to do so?

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    I also understand that the gradient of the chord should be $\frac{(a+h)^n-a^n}{h}$ but how do you proceed from that? Since the actual gradient of the curve should be $nx^{n-1}$ – 2017-02-22
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    Gradient of the tangent will be the limit of the expression you just wrote as h -> 0 – 2017-02-22
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    Yes @Saksham but wouldn't that be just $\frac{0}{0}$? – 2017-02-22
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    If not can you show me how it's done? – 2017-02-22
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    No, it wouldn't be 0/0. I think you'll have to use the binomial theorem to expand (a+h)^n – 2017-02-22
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    Check this out https://www.wolframalpha.com/input/?i=lim+h-%3E+0+%5B%7B(a%2Bh)%5En+-+a%5En%7D%2Fh%5D – 2017-02-22
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    If $n \in \mathbb{Z}^{+}$ then you can use binomial expansion to get $y'= nx^{n-1}$. – 2017-02-26

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