Derivatives of Inverse Functions,Logarithmic Differentiation.Diferenciación logarítmica, Derivadas de funciones inversas
Derivadas de funciones inversas Si y = f (x) y x = ƒ -1 (y) son diferenciables las funciones inversas, y luego sus derivados son recíprocos:
Diferenciación logarítmica
A menudo es ventajoso el uso de logaritmos para diferenciar determinadas funciones.
1. En tomar de ambas partes
2. Diferenciar
3. Resolver y '
4. Y sustituto de
5. Simplificar
Derivatives of Inverse Functions
If y = ƒ(x) and x = ƒ-1(y) are differentiable inverse functions, then their derivatives are reciprocals:
Logarithmic Differentiation
It is often advantageous to use logarithms to differentiate certain functions.
1. Take ln of both sides
2. Differentiate
3. Solve for y'
4. Substitute for y
5. Simplify
Exercise:
for y =
ln y = [ln(x2 + 1) - ln(x2
=
y' =
y' =
A menudo es ventajoso el uso de logaritmos para diferenciar determinadas funciones.
1. En tomar de ambas partes
2. Diferenciar
3. Resolver y '
4. Y sustituto de
5. Simplificar
Ejercicio: | Encontrar de y = |
ln y = [Ln (x 2 + 1) - ln (x 2 - 1)] | |
= | |
y '= | |
y '= |
Derivatives of Inverse Functions
If y = ƒ(x) and x = ƒ-1(y) are differentiable inverse functions, then their derivatives are reciprocals:
Logarithmic Differentiation
It is often advantageous to use logarithms to differentiate certain functions.
1. Take ln of both sides
2. Differentiate
3. Solve for y'
4. Substitute for y
5. Simplify
Exercise:
for y =
ln y = [ln(x2 + 1) - ln(x2
=
y' =
y' =
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