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#1476 Mathematics Derivatives
SA REMEMBER 2025 AISSCE(Board Exam)
KNOWLEDGE 3 Marks
Differentiate $y=\sqrt{\log\left\{\sin\left(\frac{x^{3}}{3}-1\right)\right\}}$ with respect to x.
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#1468 Mathematics Derivatives
VSA UNDERSTAND 2025 AISSCE(Board Exam)
KNOWLEDGE 2 Marks
If $-2x^{2}-5xy+y^{3}=76$, then find $\frac{dy}{dx}$.
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#1467 Mathematics Derivatives
VSA APPLY 2025 AISSCE(Board Exam)
KNOWLEDGE 2 Marks
Differentiate $\left(\frac{5^{x}}{x^{5}}\right)$ with respect to x.
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#1452 Mathematics Derivatives
SA REMEMBER 2025 AISSCE(Board Exam)
KNOWLEDGE 3 Marks
Differentiate $y=\cos^{-1}\left(\frac{1-x^{2}}{1+x^{2}}\right)$ with respect to x, when $x\in(0,1)$.
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#1451 Mathematics Derivatives
SA UNDERSTAND 2025 AISSCE(Board Exam)
KNOWLEDGE 3 Marks
Differentiate $y=\sin^{-1}(3x-4x^{3})$ w.r.t. x, if $x\in[-\frac{1}{2},\frac{1}{2}]$.
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#1445 Mathematics Derivatives
VSA UNDERSTAND 2025 AISSCE(Board Exam)
KNOWLEDGE 2 Marks
If $(x)^{y}=(y)^{x}$, then find $\frac{dy}{dx}$.
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#1444 Mathematics Derivatives
VSA APPLY 2025 AISSCE(Board Exam)
Competency 2 Marks
Differentiate $\sqrt{e^{\sqrt{2x}}}$ with respect to $e^{\sqrt{2x}}$ for $x>0$.
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#1440 Mathematics Derivatives
LA UNDERSTAND 2025 AISSCE(Board Exam)
KNOWLEDGE 5 Marks
Find $\frac{dy}{dx}$ if $y^{x}+x^{y}+x^{x}=a^{b}$, where a and b are constants.
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#1439 Mathematics Derivatives
LA REMEMBER 2025 AISSCE(Board Exam)
Competency 5 Marks
For a positive constant 'a', differentiate $a^{t+\frac{1}{t}}$ with respect to $(t+\frac{1}{t})^{a}$ where t is a non-zero real number.
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#1424 Mathematics Derivatives
VSA UNDERSTAND 2025 AISSCE(Board Exam)
KNOWLEDGE 2 Marks
If $y=5\cos x-3\sin x$, prove that $\frac{d^{2}y}{dx^{2}}+y=0$.
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#1423 Mathematics Derivatives
VSA UNDERSTAND 2025 AISSCE(Board Exam)
KNOWLEDGE 2 Marks
Differentiate $\frac{\sin x}{\sqrt{\cos x}}$ with respect to x.
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#1389 Mathematics Derivatives
SA UNDERSTAND 2025 AISSCE(Board Exam)
KNOWLEDGE 3 Marks
If $x\sqrt{1+y}+y\sqrt{1+x}=0$, $-1<x<1$, $x\ne y$ then prove that $\frac{dy}{dx}=\frac{-1}{(1+x)^{2}}$.
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#1388 Mathematics Derivatives
SA REMEMBER 2025 AISSCE(Board Exam)
KNOWLEDGE 3 Marks
If $y=\log(\sqrt{x}+\frac{1}{\sqrt{x}})^{2}$, then show that $x(x+1)^{2}y_{2}+(x+1)^{2}y_{1}=2$.
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#1382 Mathematics Derivatives
VSA UNDERSTAND 2025 AISSCE(Board Exam)
KNOWLEDGE 2 Marks
If $x=e^{\frac{x}{y}}$, then prove that $\frac{dy}{dx}=\frac{x-y}{x\log x}$.
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#1372 Mathematics Derivatives
LA REMEMBER 2025 AISSCE(Board Exam)
KNOWLEDGE 5 Marks
If $x=a\left(\cos\theta+\log\tan\frac{\theta}{2}\right)$ and $y=\sin\theta$, then find $\frac{d^{2}y}{dx^{2}}$ at $\theta=\frac{\pi}{4}$.
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#1371 Mathematics Derivatives
LA REMEMBER 2025 AISSCE(Board Exam)
KNOWLEDGE 5 Marks
If $\sqrt{1-x^{2}}+\sqrt{1-y^{2}}=a(x-y)$, then prove that $\frac{dy}{dx}=\sqrt{\frac{1-y^{2}}{1-x^{2}}}$.
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#1356 Mathematics Derivatives
VSA APPLY 2025 AISSCE(Board Exam)
KNOWLEDGE 2 Marks
If $\tan^{-1}(x^{2}+y^{2})=a^{2}$, then find $\frac{dy}{dx}$.
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#1355 Mathematics Derivatives
VSA UNDERSTAND 2025 AISSCE(Board Exam)
KNOWLEDGE 2 Marks
Differentiate $2^{\cos^{2}x}$ w.r.t $\cos^{2}x$.
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#1342 Mathematics Derivatives
SA REMEMBER 2024 AISSCE(Board Exam)
KNOWLEDGE 3 Marks
If $x=a~sin^{3}\theta$, $y=b~cos^{3}\theta$ then find $\frac{d^{2}y}{dx^{2}}$ at $\theta=\frac{\pi}{4}$
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#1341 Mathematics Derivatives
SA REMEMBER 2024 AISSCE(Board Exam)
KNOWLEDGE 3 Marks
If $\sqrt{1-x^{2}}+\sqrt{1-y^{2}}=a(x-y)$, prove that $\frac{dy}{dx}=\sqrt{\frac{1-y^{2}}{1-x^{2}}}$
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