Lesson: Partial Derivatives

In this lesson, we will learn how to find the partial derivatives of functions.

Worksheet: Partial Derivatives • 25 Questions

Q1:

Find the first partial derivative of the function 𝑓 ( 𝑥 ) = 𝑥 + 𝑦 4 3 2 with respect to 𝑥 .

Q2:

Find the first partial derivative with respect to 𝑦 of 𝑓 ( 𝑥 , 𝑦 , 𝑧 ) = 𝑥 𝑦 𝑧 + 2 𝑦 𝑧 3 2 .

Q3:

Find the first partial derivative with respect to 𝑥 of the function 𝑓 ( 𝑥 , 𝑦 ) = 𝑥 + 2 𝑦 .

Q4:

Find the first partial derivative with respect to 𝑦 of the function 𝑓 ( 𝑥 , 𝑦 ) = 𝑥 + 2 𝑦 .

Q5:

Find the first partial derivative with respect to 𝑥 of the function 𝑓 ( 𝑥 , 𝑦 ) = 𝑥 + 𝑦 2 2 .

Q6:

Find the first partial derivative with respect to 𝑦 of the function 𝑓 ( 𝑥 , 𝑦 ) = 𝑥 𝑦 + 6 𝑥 𝑦 + 4 𝑥 8 𝑦 + 2 2 2 .

Q7:

Find the first partial derivative with respect to 𝑥 of the function 𝑓 ( 𝑥 , 𝑦 ) = 𝑥 + 5 𝑥 𝑦 4 3 .

Q8:

Find the first partial derivative with respect to 𝑦 of 𝑓 ( 𝑥 , 𝑦 ) = 𝑥 𝑦 3 𝑦 2 4 .

Q9:

Find the first partial derivative with respect to 𝑥 of the function 𝑓 ( 𝑥 , 𝑦 ) = 𝑒 + 𝑥 𝑦 .

Q10:

Find the first partial derivative with respect to 𝑦 of the function 𝑓 ( 𝑥 , 𝑦 ) = 𝑥 4 .

Q11:

Find the first partial derivative with respect to 𝑦 of the function 𝑓 ( 𝑥 , 𝑦 , 𝑧 ) = ( 𝑥 + 2 𝑦 + 3 𝑧 ) l n .

Q12:

Find the first partial derivative with respect to 𝑥 of the function 𝑓 ( 𝑥 , 𝑦 ) = 𝑦 𝑒 2 𝑥 .

Q13:

Find the first partial derivative of the function 𝑓 ( 𝑥 , 𝑦 ) = 𝑒 𝑥 + 𝑦 𝑦 2 with respect to 𝑥 .

Q14:

Find the first partial derivative with respect to 𝑥 of the function.

Q15:

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

Q16:

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

Q17:

Find the first partial derivative with respect to 𝑦 of 𝑓 ( 𝑥 , 𝑦 ) = 𝑥 ( 𝑥 + 𝑦 ) 2 .

Q18:

Find the first partial derivative with respect to 𝑥 of the function 𝑓 ( 𝑥 , 𝑦 ) = 𝑥 + 𝑦 + 4 .

Q19:

Find the first partial derivative with respect to 𝑦 of 𝑓 ( 𝑥 , 𝑦 , 𝑧 ) = 𝑥 + 𝑦 𝑧 4 2 c o s .

Q20:

Find, with respect to 𝑥 , the first partial derivative of 𝑓 ( 𝑥 , 𝑦 , 𝑧 , 𝑡 ) = 𝛼 𝑥 + 𝛽 𝑦 𝛾 𝑧 + 𝛿 𝑡 2 2 .

Q21:

Find the first partial derivative of the function 𝑓 ( 𝑥 , 𝑦 , 𝑧 ) = 𝑦 ( 𝑥 + 2 𝑧 ) t a n with respect to 𝑥 .

Q22:

Find the first partial derivative of the function 𝑓 ( 𝑥 , 𝑦 , 𝑧 ) = 𝑥 𝑦 𝑒 with respect to 𝑥 .

Q23:

Find the first partial derivative with respect to 𝑦 of 𝑓 ( 𝑥 , 𝑦 , 𝑧 ) = 𝑥 𝑦 𝑒 2 𝑥 𝑧 .

Q24:

Find the first partial derivative with respect to 𝑦 of 𝑓 ( 𝑥 , 𝑦 , 𝑧 , 𝑡 ) = 𝑥 𝑦 𝑧 𝑡 2 c o s .

Q25:

Find the first partial derivative with respect to 𝑧 of the function 𝑓 ( 𝑥 , 𝑦 , 𝑧 , 𝑡 ) = 𝑥 𝑦 𝑧 𝑡 2 c o s .

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