Let w = f(x, y), where x and y are functions of t. Then, according to the chain rule, \[\frac{{{\rm{dw}}}}{{{\rm{dt}}}}\] is equal
A. \[\frac{{{\rm{dw}}}}{{{\rm{dx}}}}\frac{{{\rm{dx}}}}{{{\rm{dt}}}} + \frac{{{\rm{dw}}}}{{{\rm{dy}}}}\frac{{{\rm{dt}}}}{{{\rm{dt}}}}\]
B. \[\frac{{\partial {\rm{w}}}}{{\partial {\rm{x}}}}\frac{{\partial {\rm{x}}}}{{\partial {\rm{t}}}} + \frac{{\partial {\rm{w}}}}{{\partial {\rm{y}}}}\frac{{\partial {\rm{y}}}}{{\partial {\rm{t}}}}\]
C. \[\frac{{\partial {\rm{w}}}}{{\partial {\rm{x}}}}\frac{{{\rm{dx}}}}{{{\rm{dt}}}} + \frac{{\partial {\rm{w}}}}{{\partial {\rm{y}}}}\frac{{{\rm{dy}}}}{{{\rm{dt}}}}\]
D. \[\frac{{{\rm{dw}}}}{{{\rm{dx}}}}\frac{{\partial {\rm{x}}}}{{\partial {\rm{t}}}} + \frac{{{\rm{dw}}}}{{{\rm{dy}}}}\frac{{\partial {\rm{y}}}}{{\partial {\rm{t}}}}\]
Answer: Option C
This Question Belongs to Engineering Maths >> Calculus
The Taylor series expansion of 3 sinx + 2 cosx is . . . . . . . .
A. 2 + 3x - x2 - \[\frac{{{{\text{x}}^3}}}{2}\] + ...
B. 2 - 3x + x2 - \[\frac{{{{\text{x}}^3}}}{2}\] + ...
C. 2 + 3x + x2 + \[\frac{{{{\text{x}}^3}}}{2}\] + ...
D. 2 - 3x - x2 + \[\frac{{{{\text{x}}^3}}}{2}\] + ...
A. 0
B. \[\infty \]
C. \[\frac{1}{2}\]
D. \[ - \infty \]
A. \[1 + \frac{{{{\left( {{\text{x}} - \pi } \right)}^2}}}{{3!}} + ...\]
B. \[ - 1 - \frac{{{{\left( {{\text{x}} - \pi } \right)}^2}}}{{3!}} + ...\]
C. \[1 - \frac{{{{\left( {{\text{x}} - \pi } \right)}^2}}}{{3!}} + ...\]
D. \[ - 1 + \frac{{{{\left( {{\text{x}} - \pi } \right)}^2}}}{{3!}} + ...\]
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