Integration and Differentiation In Exercises 5 and 6, verify the statement by showing that the derivative of the right side equals the integrand on the left side. ∫ ( − 6 x 4 ) d x = 2 x 3 + C
Integration and Differentiation In Exercises 5 and 6, verify the statement by showing that the derivative of the right side equals the integrand on the left side. ∫ ( − 6 x 4 ) d x = 2 x 3 + C
Solution Summary: The author proves that the derivative of the right-hand side equals to the integrand on the left side.
Integration and Differentiation In Exercises 5 and 6, verify the statement by showing that the derivative of the right side equals the integrand on the left side.
∫
(
−
6
x
4
)
d
x
=
2
x
3
+
C
With integration, one of the major concepts of calculus. Differentiation is the derivative or rate of change of a function with respect to the independent variable.
For each given function f(x) find f'(x) using the rules learned in section 9.5.
1. f(x)=x32
32x
2. f(x)=7x+13
3. f(x) =
x4
4. f(x) = √√x³
5. f(x) = 3x²+
3
x2
Find:
lim x →-6 f (x)
limx-4 f (x)
lim x-1 f (x)
lim x →4 f (x)
(-6,3) •
(-1,5)
-8
-7
(-6,-2)
4+
(4,5)
(4,2) •
(-1,1)
-6
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.