TS EAMCET · Maths · Differentiation
If \(u \equiv u(x, y)=\sin (y+a x)-(y+a x)^2\), then it implies
- A \(u_{x x}=a^2 \cdot u_{y y}\)
- B \(u_{y y}=a^2 u_{x x}\)
- C \(u_{x x}=-a^2 \cdot u_{y y}\)
- D \(u_{y y}=-a^2 u_{x x}\)
Answer & Solution
Correct Answer
(A) \(u_{x x}=a^2 \cdot u_{y y}\)
Step-by-step Solution
Detailed explanation
\(\text{Let } z = y+ax\) \(u_x = \frac{du}{dz} \frac{\partial z}{\partial x} = (\cos z - 2z)a\) \(u_{xx} = \frac{d}{dz} ((\cos z - 2z)a) \frac{\partial z}{\partial x} = a(-\sin z - 2)a = a^2(-\sin(y+ax)-2)\)…
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