Question

4. Find the derivative of the function at $P_0$ in the direction of u. 1). $h(x, y) = \tan^{-1}(y/x) + \sqrt{3}\sin^{-1}(xy/2)$, $P_0(1,1)$, $u = 3i - 2j$. 2). $h(x, y, z) = \cos xy + e^{yz} + \ln zx$, $P_0(1,0,1/2)$, $u = i + 2j + 2k$.

          4. Find the derivative of the function at $P_0$ in the direction of u.
1). $h(x, y) = \tan^{-1}(y/x) + \sqrt{3}\sin^{-1}(xy/2)$, $P_0(1,1)$, $u = 3i - 2j$.
2). $h(x, y, z) = \cos xy + e^{yz} + \ln zx$, $P_0(1,0,1/2)$, $u = i + 2j + 2k$.

4. Find the derivative of the function at P0 in the direction of u.
1). h(x, y) = tan^-1(y/x) + √(3)sin^-1(xy/2), P0(1,1), u = 3i - 2j.
2). h(x, y, z) = cos xy + e^yz + ln zx, P0(1,0,1/2), u = i + 2j + 2k.

Added by Shannon C.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Darryl Burns

Step 1

The directional derivative is given by the dot product of the gradient of the function and the unit vector in the direction of u. First, let's find the gradient of the function h(r, y). The gradient is a vector that contains the partial derivatives of the Show more…

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Find the derivative of the function at P0 in the direction of u 1). h(r, y) = tan^(-1)(y/x) + âˆš3sin^(-1)(xy/2), P0(1,1), u = 3i - 2j 2). h(x, y, z) = cos(ry) + eyz + ln(zx), P0(1,0,1/2), u = i + 2j + 2k.