Differentiation — Important Questions
Maharashtra Board · Class 12 · Mathematics & Statistics -Commerce
42 important questions from Differentiation for Maharashtra Board Class 12 Mathematics & Statistics -Commerce, with answers.
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Important Questions from Differentiation
Which of the following are correct for logarithmic differentiation? (Select all correct)
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For y = x^x, take log of both sides first, d/dx(log y) = (1/y) × (dy/dx), For y = f(x)^g(x), use logarithmic differentiation, log(m/n) = log m - log n
Logarithmic differentiation is used when the variable appears in both base and exponent. The key formula is d/dx(log y) = (1/y) × (dy/dx). Also, log(m/n) = log m - log n, but log(mn) = log m + log n, not multiplication.
Find dy/dx if x² + y² = 25
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-x/y
For implicit differentiation of x² + y² = 25: Differentiate both sides with respect to x: 2x + 2y(dy/dx) = 0. Solving for dy/dx: 2y(dy/dx) = -2x, therefore dy/dx = -x/y
If x = 3t², y = 6t, find dy/dx
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1/t
For parametric functions: dx/dt = 6t and dy/dt = 6. Using the formula dy/dx = (dy/dt)/(dx/dt) = 6/(6t) = 1/t
Find d²y/dx² if y = x⁴
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12x²
First derivative: dy/dx = 4x³. Second derivative: d²y/dx² = d/dx(4x³) = 12x². This is the second-order derivative of the given function.
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