# Get help with multivariable calculus equations

Recent questions in Multivariable calculus

### I have the multivariable function $\mathrm{log}\left({y}^{2}+4{x}^{2}-4\right)$ and I have found the maximal domain to be ${x}^{2}+\frac{{y}^{2}}{4}>1$

Sam Longoria 2022-01-06 Answered

### let x be a differentiable function $x:\left[a,b\right]\to R$ which satisfies:$\frac{dx\left(t\right)}{dt}=f\left(t,x\left(t\right)\right)$$x\left(a\right)={x}_{a}$In particular I am trying to understand what $f\left(t,x\left(t\right)\right)$ means, I understand this represents a multivariable function with parameters $t$ and $x\left(t\right)$, but I can't think of what this would mean in the given context?

Walter Clyburn 2022-01-05 Answered

### Differentiation of multivariable function proof$\frac{d}{dx}{\int }_{v\left(x\right)}^{u\left(x\right)}f\left(t,x\right)dt={u}^{\prime }\left(x\right)f\left(u\left(x\right),x\right)-{v}^{\prime }\left(x\right)f\left(v\left(x\right),x\right)+{\int }_{v\left(x\right)}^{u\left(x\right)}\frac{\partial }{\partial x}f\left(t,x\right)dt$

Kathleen Rausch 2022-01-05 Answered

### Sketch the level curves for $f\left(x,y\right)={x}^{2}-y$ together with the gradient $\mathrm{\nabla }f$ at a few typical points. Write an equation for the tangent line of the level curve $f\left(x,y\right)=1$ at the point $\left(\sqrt{2},1\right)$.

Stefan Hendricks 2022-01-04 Answered

### Derivative of a multivariable function evaluate the derivative of a function $\mathbb{R}\to \mathbb{R}$ defined as $g\left(t\right)=f\left(x+t\left(y-x\right)\right)$ where $f:{\mathbb{R}}^{n}\to \mathbb{R}$ is a multivariable function and $x,y\in {\mathbb{R}}^{n}$. Prove that $g\prime \left(t\right)={\left(y-x\right)}^{T}\mathrm{\nabla }f\left(x+t\left(y-x\right)\right)$

Donald Johnson 2022-01-04 Answered

### How do you define iterations of multivariable functions? To be clear(example): If $f:{\mathbb{R}}^{2}\to \mathbb{R}$ How do you define $f\circ f,\text{or}f\circ \dots \circ f?$?

Teddy Dillard 2022-01-04 Answered

### How to find expressions for ${f}_{xx}$ and ${f}_{yy}$ for the multivariable function $f\left(x,y\right)=\mathrm{ln}\left({x}^{2}y\right)+{y}^{3}{x}^{2}$?

David Lewis 2021-12-17 Answered

### On the final examination in Engineering Data Analysis, the mean was 72 and the standard deviation was 15. a. Determine the standard scores (z-values) of students receiving the grade of 65. b. Determine the standard scores (z-values) of students receiving the grade of 85 c. Determine the probability that a student will score greater than 75. d. Determine the probability that a student will score lower than 65. e. Find the grade corresponding to a standard score of 1.

Shelia Lawrence 2021-12-08 Answered