Math Problem Statement
Here Is The Story that happened to you earlier...
but today you're on board the spaceship #1625325007, and the captain is asking to solve tricky "ZP" (Z Planet) problem (you know what it means when captain is "asking"... that's an order):
(!!! If your answer is a fractions report it in an exact format, like 1010710107 , 2296222962)
Now, let f(x)=x^3x. Use logarithmic differentiation to determine the (ZP) derivative.
f'(x)=f′(x)=
(Enter the answer in simplified form)
f'(1)=f′(1)=
!!! The challenge is that some of the Z-Planet laws are different. In particular, "power rule" on Earth, ddxxn=nxn−1ddxxn=nxn-1 , on Z planet is "twisted" as the following:
ddxxn=n2xn−1ddxxn=n2xn-1 (ddxconst=0ddxconst=0) , and
the derivative of log function, ddxln(x)=1/x , turns into "ZP" oddness: ddxln(x)=exddxln(x)=ex .
all the other rules have not been changed.
Solution
Ask a new question for Free
By Image
Drop file here or Click Here to upload
Math Problem Analysis
Mathematical Concepts
Logarithmic Differentiation
Exponents
Product Rule
Derivative Rules
Formulas
Logarithmic identity: ln(a^b) = b ln(a)
Z-Planet Power Rule: d/dx[x^n] = n^2 x^(n-1)
Z-Planet Logarithmic Rule: d/dx[ln(x)] = e^x
Product Rule: d/dx[uv] = u'v + uv'
Theorems
Chain Rule
Logarithmic Differentiation Theorem
Suitable Grade Level
College / Advanced Calculus
Related Recommendation
Logarithmic Differentiation and Z-Planet Derivative Rules: Solve f(x) = x^{x^3}
Logarithmic Differentiation and Z Planet Rules for x^{5x} Derivative
Z-Planet Differentiation: Deriving f(x)=x^{3x} Using Logarithmic Differentiation
Z-Planet Logarithmic Differentiation of f(x)=x^3x and ZP Derivatives
Derivative Calculation on Z Planet: Using the Chain Rule for f(x) = 2e^10x^8 + 3x^5