The value of (d/dx)[xn log a xex] is

Question

The value of (d/dx)[xn log a xex] is (A)  ex log a x+(xn-1/ log e a)  (B)  exxn-1 x log a x+(1/ log e a)+n log ax  (C)  nxn-1 log a xex  (D)  xn log ax.ex

Tardigrade Admin · Accepted Answer

(d/dx)[xn. log ax.ex] =xn.(d/dx) log a x.ex + log a x.ex(d/dx)(xn) =xn log ax.(d/dx) ex+ex(d/dx) log ax +ex log a x.nxn-1 =xn ex log a x+(ex/x).(1/ log ea) +nxn-1.ex log a x =xn-1 ex x log ax+(1/ log e a) +nxn-1.ex log ax =xn-1 . ex x log ax+(1/ log e a)+n log ax

Q. The value of $\frac{d}{d x} [x^{n} lo g_{a} x e^{x}]$ is

$e^{x} lo g_{a} x + \frac{x ^{n - 1}}{l o g _{e} a}$

$e^{x} x^{n - 1} {x lo g_{a} x + \frac{1}{l o g _{e} a} + n lo g_{a} x}$

$n x^{n - 1} lo g_{a} x e^{x}$

$x^{n} lo g_{a} x . e^{x}$

Q. The value of dxd​[xnloga​xex] is

exloga​x+loge​axn−1​

exxn−1{xloga​x+loge​a1​+nloga​x}

nxn−1loga​xex

xnloga​x.ex

dxd​[xn.loga​x.ex] =xn.dxd​{loga​x.ex}+loga​x.exdxd​(xn) =xn{loga​x.dxd​ex+exdxd​loga​x} +exloga​x.nxn−1 =xn{exloga​x+xex​.loge​a1​} +nxn−1.exloga​x =xn−1ex{xloga​x+loge​a1​}+nxn−1.exloga​x =xn−1.ex{xloga​x+loge​a1​+nloga​x}

Q. The value of $\frac{d}{d x} [x^{n} lo g_{a} x e^{x}]$ is

$e^{x} lo g_{a} x + \frac{x ^{n - 1}}{l o g _{e} a}$

$e^{x} x^{n - 1} {x lo g_{a} x + \frac{1}{l o g _{e} a} + n lo g_{a} x}$

$n x^{n - 1} lo g_{a} x e^{x}$

$x^{n} lo g_{a} x . e^{x}$