For some constant a, the derivative of (xn-an/x-a) is

Question

For some constant a, the derivative of (xn-an/x-a) is (A) (n xn+a n xn-1+xn+an/(x-a)2) (B) (n xn-a n xn-1-xn+an/(x-a)2) (C) (a n xn-1-n xn-dn+xn/(x-a)2) (D) (a n xn-1-n xn-xn+dn/(x-a)2)

Tardigrade Admin · Accepted Answer

Let y=(xn-an/x-a) Differentiating y w.r.t x, we get (d y/d x)=((x-a) (d/d x)(xn-an)-(xn-an) (d/d x)(x-a)/(x-a)2) =((x-a)[n xn-1-0]-(xn-an)(1-0)/(x-a)2) =((x-a) n xn-1-xn+an/(x-a)2) =(x × n xn-1-a n xn-1-xn+an/(x-a)2) =(n xn-a n xn-1-xn+an/(x-a)2)

Q. For some constant $a$ , the derivative of $\frac{x ^{n} - a ^{n}}{x - a}$ is

$\frac{n x ^{n} + an x ^{n - 1} + x ^{n} + a ^{n}}{( x - a ) ^{2}}$

$\frac{n x ^{n} - an x ^{n - 1} - x ^{n} + a ^{n}}{( x - a ) ^{2}}$

$\frac{an x ^{n - 1} - n x ^{n} - d ^{n} + x ^{n}}{( x - a ) ^{2}}$

$\frac{an x ^{n - 1} - n x ^{n} - x ^{n} + d ^{n}}{( x - a ) ^{2}}$

Q. For some constant a, the derivative of x−axn−an​ is

(x−a)2nxn+anxn−1+xn+an​

(x−a)2nxn−anxn−1−xn+an​

(x−a)2anxn−1−nxn−dn+xn​

(x−a)2anxn−1−nxn−xn+dn​

Let y=x−axn−an​ Differentiating y w.r.t x, we get dxdy​=(x−a)2(x−a)dxd​(xn−an)−(xn−an)dxd​(x−a)​ =(x−a)2(x−a)[nxn−1−0]−(xn−an)(1−0)​ =(x−a)2(x−a)nxn−1−xn+an​ =(x−a)2x×nxn−1−anxn−1−xn+an​ =(x−a)2nxn−anxn−1−xn+an​

Q. For some constant $a$ , the derivative of $\frac{x ^{n} - a ^{n}}{x - a}$ is

$\frac{n x ^{n} + an x ^{n - 1} + x ^{n} + a ^{n}}{( x - a ) ^{2}}$

$\frac{n x ^{n} - an x ^{n - 1} - x ^{n} + a ^{n}}{( x - a ) ^{2}}$

$\frac{an x ^{n - 1} - n x ^{n} - d ^{n} + x ^{n}}{( x - a ) ^{2}}$

$\frac{an x ^{n - 1} - n x ^{n} - x ^{n} + d ^{n}}{( x - a ) ^{2}}$