Home › Previous year questions › GATE 2025 MN › Question 56GATE 2025 MN – Question 56 Engineering Mathematics · Vector Calculus · 2 marks · Numerical answer
Find the directional derivative of $f=4x^2+8y^2+9z^2$ at(3,4,5),along $2\mathbf i-3\mathbf j+4\mathbf k$,to one decimal.
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Show answer and explanation Correct answer: 39.0 to 41.0
Explanation The gradient is(8x,16y,18z),giving(24,64,90) at the point. Normalize the direction to(2,−3,4)/√29. Their dot product is(48−192+360)/√29=216/√29≈40.11,or40.1. A direction vector must be converted to unit length.
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