In online, concept of derivative is clearly explained with the help of solved example problems. In online so many websites explain the concepts with the help of math sites. 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 in online.
Concept of derivative online help example problems:
The following example problems explain the concept of derivative in online.
Example 1:
Determine the derivative by differentiating the polynomial function.
f(t) = 3t 3 +4 t 4 + 5t
Solution:
The given function is
f(t) = 3t 3 +4 t 4 + 5t
The above function is differentiated with respect to t to find the derivative
f '(t) = 3(3t 2 )+4(4t 3 ) + 5
By solving above terms
f '(t) = 9t 2 + 8t 3 + 5
Example 2:
Determine the derivative by differentiating the polynomial function.
f(t) = 6t6 + 5 t5 + 4 t4 + t
Solution:
The given equation is
f(t) = 6t6 + 5 t5 + 4 t4 + t
The above function is differentiated with respect to t to find the derivative
f '(t) = 6(6t 5) +5 (5 t4 ) +4(4 t3) + 1
By solving above terms
f '(t) = 36t 5 + 25 t4 + 16 t3 + 1
Example 3:
Determine the derivative by differentiating the polynomial function.
f(t) = 2t 2 +4 t 4 + 15
Solution:
The given function is
f(t) = 2t 2 +4t 4 + 15
The above function is differentiated with respect to t to find the derivative
f '(t) = 2(2t )+4(4 t 3 ) + 0
By solving above terms
f '(t) = 4t +16t3
Example 4:
Determine the derivative by differentiating the polynomial function.
f(t) = 5t5 +4t 4 +3t 3 + 2
Solution:
The given function is
f(t) = 5t5 +4t 4 +3t 3 + 2
The above function is differentiated with respect to t to find the derivative
f '(t) = 5(5t 4 )+4(4t 3 ) +3( 3t 2) +0
By solving above terms
f '(t) = 25t 4 +16t 3 +9 t 2
Concept of derivative online help practice problems:
1) Determine the derivative by differentiating the polynomial function.
f(t) = 2t 3 +3 t 4 + 4 t 5
Answer: f '(t) = 6t 2 +12 t3 + 20 t 4
2) Determine the derivative by differentiating the polynomial function.
f(t) = t 3+t5 + 4 t 6
Answer: f '(t) = 3t2 + 5t4 + 24 t 5
Concept of derivative online help example problems:
The following example problems explain the concept of derivative in online.
Example 1:
Determine the derivative by differentiating the polynomial function.
f(t) = 3t 3 +4 t 4 + 5t
Solution:
The given function is
f(t) = 3t 3 +4 t 4 + 5t
The above function is differentiated with respect to t to find the derivative
f '(t) = 3(3t 2 )+4(4t 3 ) + 5
By solving above terms
f '(t) = 9t 2 + 8t 3 + 5
Example 2:
Determine the derivative by differentiating the polynomial function.
f(t) = 6t6 + 5 t5 + 4 t4 + t
Solution:
The given equation is
f(t) = 6t6 + 5 t5 + 4 t4 + t
The above function is differentiated with respect to t to find the derivative
f '(t) = 6(6t 5) +5 (5 t4 ) +4(4 t3) + 1
By solving above terms
f '(t) = 36t 5 + 25 t4 + 16 t3 + 1
Example 3:
Determine the derivative by differentiating the polynomial function.
f(t) = 2t 2 +4 t 4 + 15
Solution:
The given function is
f(t) = 2t 2 +4t 4 + 15
The above function is differentiated with respect to t to find the derivative
f '(t) = 2(2t )+4(4 t 3 ) + 0
By solving above terms
f '(t) = 4t +16t3
Example 4:
Determine the derivative by differentiating the polynomial function.
f(t) = 5t5 +4t 4 +3t 3 + 2
Solution:
The given function is
f(t) = 5t5 +4t 4 +3t 3 + 2
The above function is differentiated with respect to t to find the derivative
f '(t) = 5(5t 4 )+4(4t 3 ) +3( 3t 2) +0
By solving above terms
f '(t) = 25t 4 +16t 3 +9 t 2
Concept of derivative online help practice problems:
1) Determine the derivative by differentiating the polynomial function.
f(t) = 2t 3 +3 t 4 + 4 t 5
Answer: f '(t) = 6t 2 +12 t3 + 20 t 4
2) Determine the derivative by differentiating the polynomial function.
f(t) = t 3+t5 + 4 t 6
Answer: f '(t) = 3t2 + 5t4 + 24 t 5
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