Question

Find dy/dt for the equation below. 7x^3+2xy+3y^3=3

Answer 1

dy/dt is $-\frac{(21x^2+2y)\frac{dx}{dt}}{2x+9y^2}$

What is differentiation?

Differentiation is a method of finding the derivative of a function. Differentiation is a process, in mathematics, where we find the instantaneous rate of change in function based on one of its variables. The most common example is the rate change of displacement with respect to time, called velocity.

We can find the dy/dx as shown below:

7x^3+2xy+3y^3=3

differentiating with respect to t.

$7\frac{d(x^3)}{dt} +2\frac{d(xy)}{dt}+3\frac{y^3}{dt}=0$

$7\frac{3x^2dx}{dt}+2y\frac{dx}{dt}+2x\frac{dy}{dt}+3\frac{3y^2dy}{dt}=0$

$21\frac{x^2dx}{dt}+2y\frac{dx}{dt}+2x\frac{dy}{dt}+9\frac{y^2dy}{dt}=0$

$(21x^2+2y)\frac{dx}{dt}+(2x+9y^2)\frac{dy}{dt}=0$

$(21x^2+2y)\frac{dx}{dt}=-(2x+9y^2)\frac{dy}{dt}$

$-\frac{(21x^2+2y)\frac{dx}{dt}}{2x+9y^2}=\frac{dy}{dt}$

$\frac{dy}{dt}=-\frac{(21x^2+2y)\frac{dx}{dt}}{2x+9y^2}$

Hence, dy/dt is $-\frac{(21x^2+2y)\frac{dx}{dt}}{2x+9y^2}$

Learn more about differentiations here:

brainly.com/question/25081524

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