PROBLEMS ON DIFFERENTIATION WITH RESPECT TO X

Differentiate each of the following functions with respect to x :

Problem 1 :

y = 3x² + 5x - 2

Solution :

y = 3x² + 5x - 2

Problem 2 :

y = a^x + x^a - a^a

Here a is a constant.

Solution :

y = a^x + x^a - a^a

Problem 3 :

Solution :

Problem 4 :

y = e^x ⋅ ln x

Solution :

y = e^x ⋅ ln x

Using product rule, the above function can be differentiated with respect to x.

Problem 5 :

y = 2^x ⋅ x⁵

Solution :

y = 2^x ⋅ x⁵

Using product rule, the above function can be differentiated with respect to x.

Problem 6 :

Solution :

Using quotient rule, the above function can be differentiated with respect to x.

Problem 7 :

Solution :

Using quotient rule, the above function can be differentiated with respect to x.

Problem 8 :

y = 2^x ⋅ ln x

Solution :

y = 2^x ⋅ ln x

Using product rule, the above function can be differentiated with respect to x.

Problem 9 :

Solution :

Using quotient rule, the above function can be differentiated with respect to x.

Problem 10 :

Solution :

Using chain rule, the above function can be differentiated with respect to x.

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