What is the 13th derivative of y = 12x^13 - x^11 + 4x^10?

Question

What is the 13th derivative of y = 12x^13 - x^11 + 4x^10?

Is it a factorial? Or do I have to go through each step?

Answer 1

Note that $\frac{d^n}{dx^n} x^n= n!$. So the other terms vanish and all you are left with is $12\cdot 13!$

Answer 2

notice that if you have $$\frac{d^{n}}{dx^{n}} ax^k= 0$$ if $n \ge k+1$ because in each derivation the exponent is reduced by one and fianlly you have a derivate of a constant that its 0in the derivate (n-k-1).So knowing this we can say that the last two terms become zero.Therefore we only need to calculate the derivative 13 of the first term. we can use the idntity that $\frac{d}{dx} x^k= kx^{k-1}$ and that $\frac{d}{dx} k\cdot f(x)= k\cdot\frac{d}{dx}f(x)$. So applying this you can see a pattern and finally see that this term is equal to $12\cdot13\cdot12\cdot11 ...\cdot2\cdot1$ or $12\cdot13!$ Thanks you for reading and goodbye.