Calculus Archive: Questions from March 31, 2023
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Finding Directional Derivatives In Exercises 11-18, find the derivative of the function at \( P_{0} \) in the direction of \( \mathbf{u} \). 11. \( f(x, y)=2 x y-3 y^{2}, \quad P_{0}(5,5), \quad \math2 answers -
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9-36 Find the first partial derivatives of the function. 9. \( f(x, y)=x^{4}+5 x y^{3} \) 10. \( f(x, y)=x^{2} y-3 y^{4} \) 11. \( g(x, y)=x^{3} \sin y \) 12. \( g(x, t)=e^{x t} \) 13. \( z=\ln \left(2 answers -
\[ f(x)=(2 \sin x-\cos 3 x)^{3} \] a. \( 3(2 \sin x-\cos 3 x)(2 \cos x-\sin 3 x) \) b. \( (2 \sin x-\cos 3 x)^{2}(18 \cos x-9 \sin 3 x) \) c. \( (6 \sin x-\cos 3 x)(6 \cos x+3 \sin 3 x) \) d. \( (2 \s2 answers -
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Finding Directional Derivatives In Exercises 11-18, find the derivative of the function at \( P_{0} \) in the direction of \( \mathbf{u} \). 11. \( f(x, y)=2 x y-3 y^{2}, \quad P_{0}(5,5), \quad \math2 answers -
For the following vector fields, compute the following: (a) \( \nabla \times \vec{F} \), (b) \( \nabla \cdot \vec{F} \), (c) \( \nabla \cdot(\nabla \times \vec{F}),( \) d) \( \nabla \times(\nabla \cdo2 answers -
If \( \frac{d y}{d x}=\frac{1}{4} y \), what is an equation for \( y ? \) A. \( y=e^{\frac{4}{x}+C} \) B. \( y=\frac{1}{4} e^{x}+C \) C. \( y=C e^{\frac{x}{4}} \) D. \( y=e^{\frac{x}{4}}+C \) E. \( y=2 answers -
I. Halle el diferencial total a) \( z=e^{x} \operatorname{sen}(y) \) b) \( w=\frac{x+y}{z-3 y} \) II. Considere la función \( f(x, y)=y e^{x} \) y trabaje: a) Evaluar \( f(2,1) \) y \( f(2.1,1.05) \)2 answers -
Find all possible functions with the given derivative. a. \( y^{\prime}=\frac{1}{9 \sqrt{x}} \) b. \( y^{\prime}=10 x-\frac{1}{8 \sqrt{x}} \)2 answers -
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Find all the second partial derivatives. \[ \begin{array}{l} f(x, y)=x^{4} y^{4}+4 x^{7} y \\ f_{x x}(x, y)= \\ f_{x y}(x, y)= \\ f_{y x}(x, y)= \\ f_{y y}(x, y)= \end{array} \]2 answers -
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