Let $f(x,y,z)=(x^2\cos (yz), \sin (x^2y)-x, e^{y \sin z})$. Compute the derivative matrix $Df$.
Let $f(x,y,z)=(x^2\cos (yz), \sin (x^2y)-x, e^{y \sin z})$. Compute the derivative matrix $Df$.
Answer
We have
\[\begin{pmatrix} 2x \cos (yz)& -x^2z \sin (yz) & -x^2 y \sin (yz) \\ 2x y \cos (x^2y) -1& x^2\cos (x^2y) & 0 \\ 0 & \sin z e^{y \sin z} & y\cos z e^{y \sin z} \end{pmatrix}. \]
Note that
- the firts row is partial derivatives of $x^2 \cos (yz)$ with respect to $x,y,$ and $z$, respectively.
- the second row is partial derivatives of $\sin (x^2y)-x$ with respect to $x,y,$ and $z$, respectively.
- the third row is partial derivatives of $e^{y\sin z}$ with respect to $x,y,$ and $z$, respectively.
-
Let me know if you have any questions.
The answer is accepted.
Join Matchmaticians Affiliate Marketing
Program to earn up to 50% commission on every question your affiliated users ask or answer.
- answered
- 439 views
- $5.00
Related Questions
- Show that $\int_\Omega \Delta f g = \int_\Omega f \Delta g$ for appropriate boundary conditions on $f$ or $g$
- Write a Proof
- Algebra 1 Word Problem #3
- Solve the attached problem
- Find $\lim _{x \rightarrow 0} x^{x}$
- Linear Algebra - Matrices (Multiple Choice Question) (1st Year College)
- Find all values of x... (Infinite Sums)
- Find the derivative of $f(x)=\int_{\ln x}^{\sin x} \cos u du$