Worksheet: Partial Derivatives and the Fundamental Theorem of Calculus

In this worksheet, we will practice finding the partial derivative of a function defined by an integral by applying the fundamental theorem of calculus and Leibniz integral rule.

Q1:

Find the first partial derivative with respect to 𝑥 of the function 𝐹(𝑥,𝑦)=𝑒𝑡.cosd

  • Acos(𝑒)
  • B(𝑒)sin
  • C(𝑒)cos
  • Dsin(𝑒)
  • Ecos(𝑒)

Q2:

Find the first partial derivative with respect to 𝑦 of the function 𝐹(𝑥,𝑦)=𝑒𝑡.cosd

  • A(𝑒)cos
  • Bsin(𝑒)
  • Ccos(𝑒)
  • Dcos(𝑒)
  • E(𝑒)sin

Q3:

Find the first partial derivative with respect to 𝑦 of the function 𝐹(𝑥,𝑦)=𝑡+1𝑡.d

  • A𝑥+1
  • B𝑥+1
  • C𝑦+1
  • D𝑡+1
  • E𝑦+1

Q4:

Find the first partial derivative with respect to 𝑥 of the function 𝐹(𝑥,𝑦)=𝑡+1𝑡.d

  • A𝑥+1
  • B𝑡+1
  • C𝑦+1
  • D𝑦+1
  • E𝑥+1

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