asked 2021-05-29

Find the directional derivative of f at the given point in the direction indicated by the angle theta. \(f(x,y)=ye^{-x}, (0,4), \theta=\frac{2\pi}{3}\)

asked 2021-05-13

Find the derivative \(y=\frac{\ln x}{x^6}\)

\(y=e^{x^5}\ln x\)

Find the indicated derivative of the function.

\(\frac{d^4 y}{dx^4} \text{ of } y=2x^5-3x^2-5x+1\)

\(y=e^{x^5}\ln x\)

Find the indicated derivative of the function.

\(\frac{d^4 y}{dx^4} \text{ of } y=2x^5-3x^2-5x+1\)

asked 2021-05-28

The curvature of a plane curve y=y(x) is given by the formula

\(\frac{y"(x)}{((1+(y'))^2)^{\frac{3}{2}}}\)

Find all curves for which the curvature is 1 at every point. What are these curves?

\(\frac{y"(x)}{((1+(y'))^2)^{\frac{3}{2}}}\)

Find all curves for which the curvature is 1 at every point. What are these curves?

asked 2021-05-28

Find the maximum rate of change off at the given point and the direction in which it occurs.

\(f(x, y) = 4y \sqrt{x}, (4,1)\)

\(f(x, y) = 4y \sqrt{x}, (4,1)\)

asked 2021-05-03

Describe in words the surface whose equation is given. (assume that r is not negative.) \(\theta=\frac{\pi}{4}\)

a) The plane \(y = −z\) where y is not negative

b) The plane \(y = z\) where y and z are not negative

c) The plane \(y = x\) where x and y are not negative

d) The plane \(y = −x\) where y is not negative

e) The plane \(x = z\) where x and y are not negative

a) The plane \(y = −z\) where y is not negative

b) The plane \(y = z\) where y and z are not negative

c) The plane \(y = x\) where x and y are not negative

d) The plane \(y = −x\) where y is not negative

e) The plane \(x = z\) where x and y are not negative

asked 2021-06-09

Find the derivative of the function.

\(f(\theta) = \cos(\theta^2)\)

\(f(\theta) = \cos(\theta^2)\)

asked 2021-05-22

Find the equation of the tangent plane to the graph of \(\displaystyle{f{{\left({x},{y}\right)}}}={8}{x}^{{{2}}}-{2}{x}{y}^{{{2}}}\) at the point (5,4).

A)z=23x-15y+42

B)z=48x-80y+120

C)0=48x-80y+120

D)0=23x-15y+42

A)z=23x-15y+42

B)z=48x-80y+120

C)0=48x-80y+120

D)0=23x-15y+42

asked 2021-05-22

Find the 3rd derivative of the function y=f(x) given by the equation \(\displaystyle{y}^{{{2}}}={2}{x}\).

asked 2021-05-23

Use the given graph to estimate the value of each derivative.(Round all answers to one decimal place.)
Graph uploaded below.

(a) f ' (0) 1

(b) f ' (1) 2

(c) f ' (2) 3

(d) f ' (3) 4

(e) f ' (4) 5

(f) f ' (5) 6

(a) f ' (0) 1

(b) f ' (1) 2

(c) f ' (2) 3

(d) f ' (3) 4

(e) f ' (4) 5

(f) f ' (5) 6

asked 2021-05-11

Find the derivative of

\(\displaystyle{f{{\left({x}\right)}}}={\left({x}+{4}\right)}{e}^{{{\left({5}{x}\right)}}}\)

\(\displaystyle{f{{\left({x}\right)}}}={\left({x}+{4}\right)}{e}^{{{\left({5}{x}\right)}}}\)