Differentiation Meaning
Differentiation is one of the essential parts in calculus whereas it means calculating the rate of change of a quantity with respect to change in the input quantity. As the meaning says the differentiation is also called as derivatives. Generally calculus is separated into two types namely differential calculus and integral calculus. Differential calculus or derivative is mainly used to measure the rate of change of the given function with the basis of known function value. The following are the example problems explain the meaning of differentiation.
Differentiation example problems:
The following are the example problems which explain the meaning of differentiation.
Example 1:
Reduce the given function using differentiation.
f(s) = s 5 – 2 s 4 + 18s
Solution:
The given function is
f(s) = s 5 – 2 s 4 + 18s
Differentiate the above equation with respect to s.
dy / ds = 5s 4 – 2(4 s 3 ) + 18
dy / ds = 5s 4 – 8 s 2 + 18
Understanding Implicit Differentiation is always challenging for me but thanks to all math help websites to help me out.
Example 2:
Reduce the given function using differentiation.
f(s) = s4 – 3s 3 – 4s 2 +5 s + 4
Solution:
The given function is
f(s) = s4 – 3s 3 – 4 s 2 + 5s + 4
Differentiate the above equation with respect to s.
dy / ds = 4 s 3 – 3(3s 2 ) – 4( 2 s ) + 5
dy / ds = 4 s 3 – 9s 2 – 8 s + 5
Example 3:
Reduce the given function using differentiation.
f(s) = 2s 3 – 5 s 2 + 10s
Solution:
The given function is
f(s) = 2s 3 – 5 s 2 + 10s
Differentiate the above equation with respect to s.
dy / ds = 6s 2 – 5(2 s ) + 10
dy / ds = 6s 2 – 10 s + 10
Example 4:
Reduce the given function using differentiation.
f(s) = 2s2 – 5s + 8
Solution:
The given function is
y = f(s) = 2s 2 – 5s + 8
Differentiate the above equation with respect to s.
dy / ds = 4 s – 5
Between, if you have problem on these topics Numerical Differentiation, please browse expert math related websites for more help on solve math problems step by step.
Differentiation practice problems:
The following are the practice problem which shows the meaning of differentiation.
1) Reduce the given function using differentiation.
f(s) = 4s 3 – 7 s 2 + 11s
Answer: dy / ds = 12s 2 – 14 s + 11
2) Reduce the given function using differentiation.
f(s) = 5s 2 – 4 s + 33
Answer: dy / ds = 10s – 4
Differentiation example problems:
The following are the example problems which explain the meaning of differentiation.
Example 1:
Reduce the given function using differentiation.
f(s) = s 5 – 2 s 4 + 18s
Solution:
The given function is
f(s) = s 5 – 2 s 4 + 18s
Differentiate the above equation with respect to s.
dy / ds = 5s 4 – 2(4 s 3 ) + 18
dy / ds = 5s 4 – 8 s 2 + 18
Understanding Implicit Differentiation is always challenging for me but thanks to all math help websites to help me out.
Example 2:
Reduce the given function using differentiation.
f(s) = s4 – 3s 3 – 4s 2 +5 s + 4
Solution:
The given function is
f(s) = s4 – 3s 3 – 4 s 2 + 5s + 4
Differentiate the above equation with respect to s.
dy / ds = 4 s 3 – 3(3s 2 ) – 4( 2 s ) + 5
dy / ds = 4 s 3 – 9s 2 – 8 s + 5
Example 3:
Reduce the given function using differentiation.
f(s) = 2s 3 – 5 s 2 + 10s
Solution:
The given function is
f(s) = 2s 3 – 5 s 2 + 10s
Differentiate the above equation with respect to s.
dy / ds = 6s 2 – 5(2 s ) + 10
dy / ds = 6s 2 – 10 s + 10
Example 4:
Reduce the given function using differentiation.
f(s) = 2s2 – 5s + 8
Solution:
The given function is
y = f(s) = 2s 2 – 5s + 8
Differentiate the above equation with respect to s.
dy / ds = 4 s – 5
Between, if you have problem on these topics Numerical Differentiation, please browse expert math related websites for more help on solve math problems step by step.
Differentiation practice problems:
The following are the practice problem which shows the meaning of differentiation.
1) Reduce the given function using differentiation.
f(s) = 4s 3 – 7 s 2 + 11s
Answer: dy / ds = 12s 2 – 14 s + 11
2) Reduce the given function using differentiation.
f(s) = 5s 2 – 4 s + 33
Answer: dy / ds = 10s – 4