Question
Find an equation of the tangent to the given curve at the given point.$$2 x^{2}+3 y^{2}=5 \text { at }(1,1)$$
Step 1
We use implicit differentiation to do this. The derivative of $2x^2$ is $4x$ and the derivative of $3y^2$ is $6y \frac{dy}{dx}$. The derivative of a constant is zero. So, we have: \[4x + 6y \frac{dy}{dx} = 0\] Show more…
Show all steps
Your feedback will help us improve your experience
Charles Machakwa and 78 other Calculus 1 / AB educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
Find the slope of the tangent to the curve at the point specified. $$x^{3}+5 x^{2} y+2 y^{2}=4 y+11 \text { at }(1,2)$$
Short-Cuts to Differentiation
Implicit Functions
Find an equation of the straight line tangent to the given curve at the point indicated. $$y=2 x^{2}-5 \text { at }(2,3)$$
Differentiation
Tangent Lines and Their Slopes
Determine the equation of the tangent to the curve $y=\left(x^{3}-5 x+2\right)\left(3 x^{2}-2 x\right)$ at the point (1,-2)
The Elasticity of Demand
The Product Rule
Transcript
18,000,000+
Students on Numerade
Trusted by students at 8,000+ universities
Watch the video solution with this free unlock.
EMAIL
PASSWORD