Waste less time on Facebook — follow Brilliant.
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, conceptual quizzes.
Our wiki is made for math and science
Master advanced concepts through explanations,
examples, and problems from the community.
Used and loved by 4 million people
Learn from a vibrant community of students and enthusiasts,
including olympiad champions, researchers, and professionals.
Back to all chapters
Implicit Differentiation
Not all equations can be written like y = f(x), so taking the derivative can be tricky. Save the mess and do it directly with implicit differentiation.
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, conceptual quizzes.
Our wiki is made for math and science
Master advanced concepts through explanations,
examples, and problems from the community.
Used and loved by 4 million people
Learn from a vibrant community of students and enthusiasts,
including olympiad champions, researchers, and professionals.
Your answer seems reasonable.
Find out if you're right!
Sign up to access problem solutions.
That seems reasonable.
Find out if you're right!
If \[\frac { x ( x - 6y) } { 5 - 4 y^ 2 } = 1, \] what is \(\displaystyle \frac{dy}{dx}?\)
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, conceptual quizzes.
Our wiki is made for math and science
Master advanced concepts through explanations,
examples, and problems from the community.
Used and loved by 4 million people
Learn from a vibrant community of students and enthusiasts,
including olympiad champions, researchers, and professionals.
Your answer seems reasonable.
Find out if you're right!
Sign up to access problem solutions.
That seems reasonable.
Find out if you're right!
by Brilliant Staff
If \( \frac{ 3 x ^2 + 7 xy^2 } { 8 + 5 y^3 } = 1 \), what is \(\displaystyle \frac{dy}{dx}?\)
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, conceptual quizzes.
Our wiki is made for math and science
Master advanced concepts through explanations,
examples, and problems from the community.
Used and loved by 4 million people
Learn from a vibrant community of students and enthusiasts,
including olympiad champions, researchers, and professionals.
Your answer seems reasonable.
Find out if you're right!
Sign up to access problem solutions.
That seems reasonable.
Find out if you're right!
by Brilliant Staff
If point \((1,a)\) with \(a>0\) lies on the curve \[\frac{y}{x}-\frac{9x}{y}=8,\] what is the derivative \(\displaystyle \frac{dy}{dx}\) of the curve at the point?
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, conceptual quizzes.
Our wiki is made for math and science
Master advanced concepts through explanations,
examples, and problems from the community.
Used and loved by 4 million people
Learn from a vibrant community of students and enthusiasts,
including olympiad champions, researchers, and professionals.
Your answer seems reasonable.
Find out if you're right!
Sign up to access problem solutions.
That seems reasonable.
Find out if you're right!
by Brilliant Staff
Given \[\frac{(x^2+y^2-11x)^2}{x^2+y^2}=4, \] what is the value of \(\displaystyle \frac{dy}{dx}\) when \(x=0\) and \(y=2 ?\)
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, conceptual quizzes.
Our wiki is made for math and science
Master advanced concepts through explanations,
examples, and problems from the community.
Used and loved by 4 million people
Learn from a vibrant community of students and enthusiasts,
including olympiad champions, researchers, and professionals.
Your answer seems reasonable.
Find out if you're right!
Sign up to access problem solutions.
That seems reasonable.
Find out if you're right!
by Brilliant Staff
If \[\frac{6x-y^3}{y+x^2}=x+4, \] what is \(\displaystyle \frac{dy}{dx}?\)
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, conceptual quizzes.
Our wiki is made for math and science
Master advanced concepts through explanations,
examples, and problems from the community.
Used and loved by 4 million people
Learn from a vibrant community of students and enthusiasts,
including olympiad champions, researchers, and professionals.
Your answer seems reasonable.
Find out if you're right!
Sign up to access problem solutions.
That seems reasonable.
Find out if you're right!
by Brilliant Staff