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Find the derivative using logarithmic differentiation method $\frac{d}{dx}\left(\left(\left(7^x\right)^{37}\right)^{-121x}\right)$

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Solution

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Final Answer

$\ln\left(7\right)\cdot -8954\cdot 7^{-4477x^2}x$
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Step-by-step Solution

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Simplify the derivative by applying the properties of logarithms

$\frac{d}{dx}\left(7^{-4477x^2}\right)$

Learn how to solve logarithmic differentiation problems step by step online.

$\frac{d}{dx}\left(7^{-4477x^2}\right)$

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Learn how to solve logarithmic differentiation problems step by step online. Find the derivative using logarithmic differentiation method d/dx(7^x^37^(-121x)). Simplify the derivative by applying the properties of logarithms. Applying the derivative of the exponential function. Calculating the natural logarithm of 7. The derivative of a function multiplied by a constant (-4477) is equal to the constant times the derivative of the function.

Final Answer

$\ln\left(7\right)\cdot -8954\cdot 7^{-4477x^2}x$

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Solving a math problem using different methods is important because it enhances understanding, encourages critical thinking, allows for multiple solutions, and develops problem-solving strategies. Read more

Find the derivativeFind derivative of 7^x^37^-121x using the product ruleFind derivative of 7^x^37^-121x using the quotient ruleFind derivative of 7^x^37^-121x using logarithmic differentiationFind derivative of 7^x^37^-121x using the definition

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Function Plot

Plotting: $\ln\left(7\right)\cdot -8954\cdot 7^{-4477x^2}x$

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7
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9
0
a
b
c
d
f
g
m
n
u
v
w
x
y
z
.
(◻)
+
-
×
◻/◻
/
÷
◻2
◻◻
√◻
√

◻√◻
◻√
∞
e
π
ln
log
log◻
lim
d/dx
D□x
∫
∫◻
|◻|
θ
=
>
<
>=
<=
sin
cos
tan
cot
sec
csc

asin
acos
atan
acot
asec
acsc

sinh
cosh
tanh
coth
sech
csch

asinh
acosh
atanh
acoth
asech
acsch

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Main Topic: Logarithmic Differentiation

The logarithmic derivative of a function f(x) is defined by the formula f'(x)/f(x).

Used Formulas

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