JEE Mains · Maths · STD 12 - 5. continuity and differentiation
If \(y(x)=\left(x^{x^{x}}\right), x>0\) then \(\frac{d^{2} x}{d y^{2}}+20\) at \(x=1\) is equal to
- A \(06\)
- B \(16\)
- C \(26\)
- D \(36\)
Answer & Solution
Correct Answer
(B) \(16\)
Step-by-step Solution
Detailed explanation
\(y=(x)=\left(x^{x}\right)^{x}\) \(\ln y ( x )= x ^{2} \cdot \ln x\) \(\frac{1}{y(x)} \cdot y^{\prime}(x)=\frac{x^{2}}{x}+2 x \cdot \ln x\) \(y^{\prime}(x)=y(x)[x+2 x \ln x]\) \(y(1)=1 ; y^{\prime}(1)=1\)…
See the Complete Solution
Get step-by-step explanations for this and 2.5 Lakh+ more JEE, NEET & CET questions.
- Unlock all solutions
- Practice the full chapter
- Track accuracy across PYQs
4.8 rated on Google Play · 14,000+ reviews
More questions from Maths
- For \(p\,>\,0\), a vector \(\vec{v}_{2}=2 \hat{i}+(p+1) \hat{j}\) is obtained by rotating the vector \(\vec{v}_{1}=\sqrt{3} p \hat{i}+\hat{j}\) by an angle \(\theta\) about origin in counter clockwise direction. If \(\tan \theta=\frac{(\alpha \sqrt{3}-2)}{4 \sqrt{3}+3}\), then the value of \(\alpha\) is equal to \(....\)JEE Mains 2021 Hard
- Let \(f\) and \(g\) be twice differentiable functions on \(R\) such that \(f^{\prime \prime}(x)=g^{\prime \prime}(x)+6 x\) \(f^{\prime}(1)=4 g^{\prime}(1)-3=9\) \(f(2)=3 g(2)=12\) Then which of the following is NOT true ?JEE Mains 2023 Hard
- Let \(A\) be a \(3 \times 3\) matrix with \(\operatorname{det}( A )=4\). Let \(R _{ i }\) denote the \(i ^{\text {th }}\) row of \(A\). If a matrix \(B\) is obtained by performing the operation \(R _{2} \rightarrow 2 R _{2}+5 R _{3}\) on \(2 A ,\) then \(\operatorname{det}( B )\) is equal to ...... .JEE Mains 2021 Medium
- If \(\cos ec\,\theta = \frac{{p + q}}{{p - q}}\) \(\left( {p \ne q \ne 0} \right)\), then \(\left| {\cot \left( {\frac{\pi }{4} + \frac{\theta }{2}} \right)} \right|\) is equal toJEE Mains 2014 Hard
- The interval in which the function \(\mathrm{f}(\mathrm{x})=\mathrm{x}^{\mathrm{x}}, \mathrm{x}>0\), is strictly increasing isJEE Mains 2024 Medium
- Let \( f(x)=[x]^{2}-[x+3]-3, x\in\mathbb{R} \) where \( [\bullet]\) is the greatest integer function. ThenJEE Mains 2026 Easy
More PYQs from JEE Mains
- Let \(X _{1}, X _{2}, \ldots, X _{18}\) be eighteen observations such that \(\sum_{ i =1}^{18}\left( X _{ i }-\alpha\right)=36 \quad\) and \(\sum_{i=1}^{18}\left(X_{i}-\beta\right)^{2}=90,\) where \(\alpha\) and \(\beta\) are distinct real numbers. If the standard deviation of these observations is \(1,\) then the value of \(|\alpha-\beta|\) is ...... .JEE Mains 2021 Hard
- For a differentiable function \(\mathrm{f}: I R \rightarrow I R\), suppose \(f^{\prime}(\mathrm{x})=3 f(\mathrm{x})+\alpha\), where \(\alpha \in \operatorname{IR}, f(0)=1\) and \(\lim _{x \rightarrow-\infty} f(x)=7\). Then \(9 \mathrm{f}\left(-\log _{\mathrm{e}} 3\right)\) is equal to ............JEE Mains 2024 Hard
- \(\int_{\frac{3 \sqrt{2}}{4}}^{\frac{3 \sqrt{3}}{4}} \frac{48}{\sqrt{9-4 x^2}} d x\) is equal toJEE Mains 2023 Medium
- Let \(C\) be the largest circle centred at \((2,0)\) and inscribed in the ellipse \(=\frac{x^2}{36}+\frac{y^2}{16}=1\).If \((1, \alpha)\) lies on \(C\), then \(10 \alpha^2\) is equal to \(.........\)JEE Mains 2023 Hard
- Let \(P\) be the point of intersection of the common tangents to the parabola \(y^2 = 12x\) and the hyperbola \(8x^2 -y^2 = 8\). If \(S\) and \(S'\) denote the foci of the hyperbola where \(S\) lies on the positive \(x-\) axis then \(P\) divides \(SS'\) in a ratioJEE Mains 2019 Hard
- Let \(f(x)=a x^3+b x^2+c x+41\) be such that \(f(1)=40, f^{'}(1)=2\) and \(f^{''}(1)=4\). Then \(a^2+b^2+c^2\) is equal to :JEE Mains 2024 Hard