Math Problem Statement
. (a) Using Chain Rule, find (dz)/(dt) dagger the function z = sqrt(1 - x + 4x * y ^ 2) x = ln(t) y = t ^ (3/2)
Solution
Ask a new question for Free
By Image
Drop file here or Click Here to upload
Math Problem Analysis
Mathematical Concepts
Multivariable Calculus
Partial Derivatives
Chain Rule
Formulas
Chain Rule: dz/dt = (∂z/∂x)(dx/dt) + (∂z/∂y)(dy/dt)
Partial derivative of z with respect to x: ∂z/∂x = (1/2)(1 - x + 4xy^2)^(-1/2)(-1 + 4y^2)
Partial derivative of z with respect to y: ∂z/∂y = (1/2)(1 - x + 4xy^2)^(-1/2)(8xy)
Theorems
Chain Rule for multivariable functions
Suitable Grade Level
Undergraduate Calculus
Related Recommendation
Calculating the Time Derivative of a Multivariable Function Using the Chain Rule
Calculate dy/dt Using Chain Rule with Function x = √(3t + 1)
Implicit Differentiation of sqrt(x^2 + 6xy + y^6) = 2
Chain Rule in Multivariable Calculus: Finding dw/dt for w = xe^(y/z)
Differentiating ln(x^2 + y^2 + z^2) Using the Chain Rule