List of top Engineering Mathematics Questions on Differentiation

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).
Let \(f(x) = \ln x\). The first derivative \(f'(x)\) is to be calculated at \(x=1\) using numerical differentiation. \(f'(1)\) is calculated using: - First-order forward difference (\(f'_{FD}\)), - First-order backward difference (\(f'_{BD}\)), - Second-order central difference (\(f'_{CD}\)), with interval width \(h = 0.1\). The correct order of the values of \(f'_{FD}, f'_{BD}, f'_{CD}\) is:
Which of the following statement(s) is/are CORRECT?
Let \( f(x) = \ln x \). The first derivative \( f'(x) \) is to be calculated at \( x = 1 \) using numerical differentiation. \( f'(1) \) is calculated using first order forward difference (\( f'_{FD} \)), first order backward difference (\( f'_{BD} \)), and second order central difference (\( f'_{CD} \)), using interval width \( h = 0.1 \). The CORRECT order of the values of \( f'_{FD} \), \( f'_{BD} \), and \( f'_{CD} \) is:
If \( y = x^x \), then \( \frac{dy}{dx} \) is: