Calculus Archive: Questions from January 06, 2023
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2 answers
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4(c) only
4. Find \( \partial u / \partial x, \partial u / \partial y \) and show that \[ \frac{\partial^{2} u}{\partial x \partial y}=\frac{\partial^{2} u}{\partial y \partial x} \] for each of the following f2 answers -
Find \( a+b+c+d \) if \( \cos (3 x)+4 \cos (2 x)=a\left(\cos ^{3} x\right)+b\left(\cos ^{2} x\right)+c(\cos x)+d \)2 answers -
Thank you!
\( y=(x+1)^{(x+1)} \) \( y^{\prime}=x \cdot x^{(x-1)}+1 \) \( y^{\prime}=(x+1) \cdot(x+1)^{x} \) \( y^{\prime}=(x+1)^{x} \cdot \ln (x+1) \) \( y^{\prime}=(x+1)^{(x+1)} \cdot \ln (x+1) \) \( y^{\prime}2 answers -
Example (17): Solve the initial-value problem (IVP) \[ (\tan y-2) d x+\left(x \sec ^{2} y+\frac{1}{y}\right) d y=0, y(0)=1 \]2 answers -
Resuelve por el método de separación de variables los siguientes ejercicios: 5. \( y \ln x \frac{d x}{d y}=\left(\frac{y+1}{x}\right)^{2} \) 6. \( \frac{d P}{d t}=P-P^{2} \)2 answers