The function f(x) = x x satisfies the following equation: f''(x) + f(x) + t x = 0. The value of t is …

Official answer: -2. Explanation: Given: f(x) = x x Compute the first derivative f'(x) using the product rule: f'(x) = ddx(x x) = 1 x + x x = x + x x Compute the second derivative f''(x): f''(x) = ddx( x + x x) = x + (1 x - x x) = 2 x - x x Substitute f(x) and f''(x) into the given differential equation: f''(x) + f(x) + t x = 0 (2 x - x x) + (x x) + t x = 0 2 x + t x = 0 (2 + t) x = 0 For this equation to hold for all x, we must have: 2 + t = 0 t = -2 Thus, the value of t is -2.

Engineering Mathematics · Calculus

Official IIT answer key · IIT Kharagpur · Audited Aug 2026

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GATE CSE 2014 Set 1 Q46 · NAT · 2 marks

The function $f(x) = x \sin x$ satisfies the following equation: $f^{\prime}'(x) + f(x) + t \cos x = 0$ . The value of $t$ is _____.

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Key concept

Calculus

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How GATE tests Calculus

Calculus in GATE CS tests single-variable differential and integral calculus, foundational limit evaluations, continuity and differentiability of piecewise/absolute-value functions, and mean value theorems (Rolle's and LMVT). Earlier years (2012-2015) also included numerical methods such as Newton-Raphson, Bisection, and Trapezoidal/Simpson's rules, whereas recent papers (2020-2026) focus heavily on analytical properties: odd/even symmetry in single and multiple integrals, boundary extrema, points of non-differentiability, and MSQ-based structural analyses of functions.

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Independent practice explanation verified by the GateAI team. GATE is conducted by the IITs; question text follows the official paper.

Engineering Mathematics · Calculus

Official IIT answer key · IIT Kharagpur · Audited Aug 2026

Take topic test

GATE CSE 2014 Set 1 Q46 · NAT · 2 marks

The function $f(x) = x \sin x$ satisfies the following equation: $f^{\prime}'(x) + f(x) + t \cos x = 0$ . The value of $t$ is _____.

Numerical answer

Enter a value to check

Key concept

Calculus

Step-by-step verified solution

Examiner trap & misconception

Topic notes

How GATE tests Calculus

Full Calculus guide →

More on Calculus

All 40 questions on Calculus →

Independent practice explanation verified by the GateAI team. GATE is conducted by the IITs; question text follows the official paper.

The function $f(x) = x \sin x$ satisfies the following equation: $f^{\prime}'(x) + f(x) + t \cos x = 0$ . The value of $t$ is _____.

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Check you can still solve Calculus under a clock

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The function $f(x) = x \sin x$ satisfies the following equation: $f^{\prime}'(x) + f(x) + t \cos x = 0$ . The value of $t$ is _____.

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Check you can still solve Calculus under a clock

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The function f(x)=xsin⁡xf(x) = x \sin xf(x)=xsinx satisfies the following equation: f^{\prime}'(x) + f(x) + t \cos x = 0. The value of ttt is _____.

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The function f(x)=xsin⁡xf(x) = x \sin xf(x)=xsinx satisfies the following equation: f^{\prime}'(x) + f(x) + t \cos x = 0. The value of ttt is _____.

Step-by-step verified solution

Check you can still solve Calculus under a clock

More from GATE CSE 2014 Set 1

More on Calculus

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The function $f(x) = x \sin x$ satisfies the following equation: $f^{\prime}'(x) + f(x) + t \cos x = 0$ . The value of $t$ is _____.

The function $f(x) = x \sin x$ satisfies the following equation: $f^{\prime}'(x) + f(x) + t \cos x = 0$ . The value of $t$ is _____.