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Step-by-step Solution

Find the implicit derivative $\frac{d}{dx}\left(x^2+y^2=16\right)$

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Step-by-step explanation

Problem to solve:

$\frac{d}{dx}\left(x^2+y^2=16\right)$

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

$\frac{d}{dx}\left(x^2+y^2\right)=\frac{d}{dx}\left(16\right)$

Unlock this full step-by-step solution!

Learn how to solve implicit differentiation problems step by step online. Find the implicit derivative (d/dx)(x^2+y^2=16). Apply implicit differentiation by taking the derivative of both sides of the equation with respect to the differentiation variable. The derivative of the constant function (16) is equal to zero. The derivative of a sum of two functions is the sum of the derivatives of each function. The power rule for differentiation states that if n is a real number and f(x) = x^n, then f'(x) = nx^{n-1}.

Answer

$y^{\prime}=\frac{-2x}{2y}$

Problem Analysis

$\frac{d}{dx}\left(x^2+y^2=16\right)$

Related formulas:

4. See formulas

Time to solve it:

~ 0.68 seconds