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Derivative of Polynomials
Related Topics
Wize University Calculus 1 Textbook > Derivatives
The Power Rule (Derivative of Polynomials)
3 Activities
Suppose
f
is a function which satisfies
f
′
(
0
)
=
π
and
f
(
x
+
y
)
=
f
(
x
)
+
f
(
y
)
f'(0)=\pi \text{ and }f(x+y)=f(x)+f(y)
f
′
(
0
)
=
π
and
f
(
x
+
y
)
=
f
(
x
)
+
f
(
y
)
for all
x
and
y
. True or false:
f
(
x
)
=
π
x
f(x)=\pi x
f
(
x
)
=
π
x
satisfies this function.
True
False
I don't know
Check Submission
More The Power Rule (Derivative of Polynomials) Questions:
Higher Order Derivatives: The Power Rule
If
f
(
x
)
=
x
10
f\left(x\right)=x^{10}
f
(
x
)
=
x
10
find
f
(
9
)
(
x
)
f^{\left(9\right)}\left(x\right)
f
(
9
)
(
x
)
.
(i.e. the 9th derivative)
Derivative of Polynomials: Product Rule
Find the derivative of
f
(
x
)
=
(
x
3
/
2
+
2
x
)
(
x
7
/
4
+
x
)
f(x)=\left(x^{3/2}+\frac{2}{x}\right)\left(x^{7/4}+x\right)
f
(
x
)
=
(
x
3/2
+
x
2
)
(
x
7/4
+
x
)
The Power Rule: Derivatives of Polynomials
Find the derivative of
f
(
x
)
=
x
3
x
f\left(x\right)=\dfrac{x^3}{\sqrt{x}}
f
(
x
)
=
x
x
3
Derivative of Polynomials: Product Rule
Find the derivative of
f
(
x
)
=
(
x
3
/
2
+
2
x
)
(
x
7
/
4
+
x
)
f(x)=\left(x^{3/2}+\frac{2}{x}\right)\left(x^{7/4}+x\right)
f
(
x
)
=
(
x
3/2
+
x
2
)
(
x
7/4
+
x
)
Higher Order Derivatives: The Power Rule
If
f
(
x
)
=
x
10
f\left(x\right)=x^{10}
f
(
x
)
=
x
10
find
f
(
9
)
(
x
)
f^{\left(9\right)}\left(x\right)
f
(
9
)
(
x
)
.
(i.e. the 9th derivative)
Find the derivative of
f
(
x
)
=
x
3
x
f\left(x\right)=\frac{x^3}{\sqrt{x}}
f
(
x
)
=
x
x
3
The Power Rule: Derivatives of Polynomials
Find the derivative of
f
(
x
)
=
x
3
x
f\left(x\right)=\dfrac{x^3}{\sqrt{x}}
f
(
x
)
=
x
x
3
Derivative of Polynomials: Product Rule
Find the derivative of
f
(
x
)
=
(
x
3
/
2
+
2
x
)
(
x
7
/
4
+
x
)
f(x)=\left(x^{3/2}+\frac{2}{x}\right)\left(x^{7/4}+x\right)
f
(
x
)
=
(
x
3/2
+
x
2
)
(
x
7/4
+
x
)
If 𝑓(𝑥) = 𝑥
10
, find 𝑓
(9)
(𝑥).
(i.e. the 9th derivative)
Find the derivative of
f
(
x
)
=
x
3
x
f\left(x\right)=\frac{x^3}{\sqrt{x}}
f
(
x
)
=
x
x
3