Implicit Differentiation: Level 2 Challenges Practice Problems Online

Consider the function

$f(x) = \sqrt{x+\sqrt{x+\sqrt{x+\cdots}}}.$

If the gradient of the tangent of the function at $x = 12$ can be expressed as $\frac{a}{b},$ where $a$ and $b$ are coprime positive integers, what is the value of $a + b?$ .

$\sin ( x + y ) = \log ( x + y )$

Find the value of $\frac {dy}{dx}$ .

Note that we didn't give you the base of the logarithm, you should not specifically assume that the logarithm is in base $e$ or 10.

If ${ x }^{ y }={ e }^{ x-y }$ , then $\frac { dy }{ dx } = \text{\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_}.$

\frac { x-y }{ (1+\log { x)^{ 2 } } }

\frac { y-x }{ x(1+\log { x) } }

\frac { \log { x } }{ (1+\log { x)^{ 2 } } }

\frac { x-y }{ 1+\log { x } }

Which of the given equations is the common tangent to the circle ${(x-3)}^2+{y}^2=9$ and the parabola ${y}^2=4x$ touching both the conics above the $x$ -axis?

Consider the function $\displaystyle f(x) = \frac{x}{1+\frac{x}{1+\frac{x}{1+\ddots}}}.$

Determine the value of $f'(0).$

Concept Quizzes

Challenge Quizzes

Implicit Differentiation: Level 2 Challenges

Excel in math and science

Master concepts by solving fun, challenging problems.

It's hard to learn from lectures and videos

Learn more effectively through short, interactive explorations.

Used and loved by over 7 million people

Learn from a vibrant community of students and enthusiasts, including olympiad champions, researchers, and professionals.