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Step-by-step Solution

Find the derivative $\frac{d}{dx}\left(4^x-5^x+x^{-2}\right)$ using the sum rule

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Answer

$\frac{17}{\sqrt{3}}4^x-\sqrt[4]{45}5^x-2x^{-3}$

Step-by-step explanation

Problem to solve:

$\frac{d}{dx}\left(4^x-5^x+x^{-2}\right)$
1

The derivative of a sum of two functions is the sum of the derivatives of each function

$\frac{d}{dx}\left(4^x\right)+\frac{d}{dx}\left(-5^x\right)+\frac{d}{dx}\left(x^{-2}\right)$
2

The derivative of a function multiplied by a constant is equal to the constant times the derivative of the function

$\frac{d}{dx}\left(4^x\right)-\frac{d}{dx}\left(5^x\right)+\frac{d}{dx}\left(x^{-2}\right)$

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Answer

$\frac{17}{\sqrt{3}}4^x-\sqrt[4]{45}5^x-2x^{-3}$
$\frac{d}{dx}\left(4^x-5^x+x^{-2}\right)$

Main topic:

Sum rule

Used formulas:

4. See formulas

Time to solve it:

~ 0.67 seconds