the derivation of y=e^x.logx is
a) e^x[1/x+logx]
b)e^x[1/x-logx]
c)[1/x+logx]
d)[1/x-logx]
Answers
Answered by
43
EXPLANATION.
Derivation : y = eˣ ㏒(x).
As we know that,
Formula of :
Products Rule.
⇒ d/dx [f(x).g(x)] = f(x).d/dx[g(x)] + g(x).d/dx[f(x)].
Using this formula in the equation, we get.
⇒ dy/dx = eˣ.d/dx[㏒(x)] + ㏒(x).d/dx[eˣ].
⇒ dy/dx = eˣ.(1/x) + ㏒(x).eˣ.
⇒ dy/dx = eˣ[1/x + ㏒(x)].
Option [A] is correct answer.
MORE INFORMATION.
(1) d/dx (constant) = 0.
(2) d/dx (ax) = a.
(3) d/dx (xⁿ) = nxⁿ⁻¹.
(4) d/dx (eˣ) = eˣ.
(5) d/dx (aˣ) = aˣ.㏒(a).
(6) d/dx (㏒x) = 1/x.
(7) d/dx [㏒ₐ(x)] = 1/x㏒(a).
Answered by
17
Step-by-step explanation:
Derivation : y = eˣ ㏒(x).
As we know that,
Formula of :
Products Rule.
⇒ d/dx [f(x).g(x)] = f(x).d/dx[g(x)] + g(x).d/dx[f(x)].
Using this formula in the equation, we get.
⇒ dy/dx = eˣ.d/dx[㏒(x)] + ㏒(x).d/dx[eˣ].
⇒ dy/dx = eˣ.(1/x) + ㏒(x).eˣ.
⇒ dy/dx = eˣ[1/x + ㏒(x)].
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