Directional derivatives, SIMPLE

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f(x, y, z) = xe^y + ye^z + ze^x, at (0, 0, 0),

directional vector v = <-2, 0, 5>

i solved for gradient f = (e^y + ze^x, xe^y + e^z, ye^z + e^x), at f(0,0,0) to be...

gradient f = (1,1,1)

this would make the answer just be -2 + 0 + 5 = 3
but this isn't right.

can someone show me what i did wrong?
 
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The directional derivative involves the unit vector in the direction of v, not v itself. Find the unit vector u = v/|v| and use that in your calculation.
 
thank you! that makes a lot of sense
 
Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...

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