Question

Find the derivative of Tan(x)=Tan(y)

Answer 1

Answer:

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Answer 2

The derivative of tan(x) = tan(y) is $y' = \dfrac{sec^{2}x }{sec^{2}y}$

Step-by-step explanation:

Given: tan(x) = tan(y)

To Find: derivative of tan(x) = tan(y)

Solution:

• Finding the derivative of tan(x) = tan(y)

We have given that tan(x) = tan(y), therefore, the derivative can be calculated as follows,

$\Rightarrow tan(x) = tan(y)$

Differentiating it both sides, we get,

$\Rightarrow \sec^2\left(x\right)=\sec^2\left(y\right) \cdot \dfrac{d[y]}{dx}$

$\Rightarrow \sec^2\left(x\right)=\sec^2\left(y\right)\dfrac{dy}{dx}$

$\dfrac{dy}{dx} = y'=\dfrac{\sec^2\left(x\right)}{\sec^2\left(y\right)}$

Hence, the derivative of tan(x) = tan(y) is $y' = \dfrac{sec^{2}x }{sec^{2}y}$