List of top Engineering Mathematics Questions on Differentiation asked in GATE MN

The directional derivative of a function \( f(x, y, z) = 4x^2 + 8y^2 + 9z^2 \) at the point \( P(3, 4, 5) \) in the direction vector \( \vec{b} = 2\hat{i} - 3\hat{j} + 4\hat{k} \) is _______ (rounded off to 1 decimal place).
If \( y = x^x \), then \( \frac{dy}{dx} \) is: