Concept of derivative can be easily explained with the help of solving basic problems in calculus. The derivative concept is clearly explained in calculus whereas derivative concept helps to find the rate of change for the given function with respect to change in the input function. The following are the example problems with detailed solution helps to explain the concept of derivative for study.
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Concept of derivative example problems for study:
The following example problems explain the concept of derivative to study for the exam.
Example 1:
Calculate the derivative by differentiating the given function.
f(y) = 3y 3 +4 y 4 + 5y
Solution:
The given function is
f(y) = 3y 3 +4 y 4 + 5y
The above function is differentiated with respect to y to find the derivative
f '(y) = 3(3y 2 )+4(4y 3 ) + 5
By solving above terms
f '(y) = 9y 2 + 8y 3 + 5
Example 2:
Calculate the derivative by differentiating the given function.
f(y) = 6y6 + 5 y5 + 4 y4 + y
Solution:
The given equation is
f(y) = 6y6 + 5 y5 + 4 y4 + y
The above function is differentiated with respect to y to find the derivative
f '(y) = 6(6y 5) +5 (5 y4 ) +4(4 y3) + 1
By solving above terms
f '(y) = 36y 5 + 25 y4 + 16 y3 + 1
Example 3:
Calculate the derivative by differentiating the given function.
f(y) = 2y 2 +4 y 4 + 15
Solution:
The given function is
f(y) = 2y 2 +4y 4 + 15
The above function is differentiated with respect to y to find the derivative
f '(y) = 2(2y )+4(4 y 3 ) + 0
By solving above terms
f '(y) = 4y +16y3
Example 4:
Calculate the derivative by differentiating the given function.
f(y) = 5y5 +4y 4 +3y 3 + 2
Solution:
The given function is
f(y) = 5y5 +4y 4 +3y 3 + 2
The above function is differentiated with respect to y to find the derivative
f '(y) = 5(5y 4 )+4(4y 3 ) +3( 3y 2) +0
By solving above terms
f '(y) = 25y 4 +16y 3 +9 y 2
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Concept of derivative practice problems for study:
1) Calculate the derivative by differentiating the given function.
f(y) = 2y 3 +3 y 4 + 4 y 5
Answer: f '(y) = 6y 2 +12 y3 + 20 y 4
2) Calculate the derivative by differentiating the given function.
f(y) = y 3+y5 + 4 y 6
Answer: f '(y) = 3y2 + 5y4 + 24 y 5
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