Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Let
g be a function such that
g(5)=7 and
g^(')(5)=-2.
Let
h be the function
h(x)=x.

Evaluate
(d)/(dx)[g(x)*h(x)] at
x=5.

- Let $g$ be a function such that $g(5)=7$ and $g^{\prime}(5)=-2$ . $\newline$ - Let $h$ be the function $h(x)=x$ . $\newline$ Evaluate $\frac{d}{d x}[g(x) \cdot h(x)]$ at $x=5$ .

View step-by-step help

View step-by-step help

Full solution

Q. - Let

g

be a function such that

g(5)=7

and

g^{\prime}(5)=-2

.

\newline

- Let

h

be the function

h(x)=x

.

\newline

Evaluate

\frac{d}{d x}[g(x) \cdot h(x)]

at

x=5

.

Apply Product Rule: Use the product rule for differentiation: $f * g$ ' = f' * g + f * g'.
Differentiate Functions: Differentiate $g(x)$ to get $g'(x)$ and $h(x)$ to get $h'(x)$ . $\newline$ Since $h(x) = x$ , $h'(x) = 1$ .
Evaluate Derivatives: Evaluate $g'(5)$ and $h(5)$ using the given information. $\newline$ $g'(5) = -2$ and $h(5) = 5$ .
Apply Product Rule Formula: Plug the values into the product rule formula. $\newline$ $(\frac{d}{dx})[g(x)*h(x)]$ at $x=5$ = $g'(5) * h(5) + g(5) * h'(5)$ .
Substitute Values: Substitute the known values into the equation. $\newline$ $\frac{d}{dx}[g(x)*h(x)]$ at $x=5$ = $(-2)$ * $5$ + $7$ * $1$ .
Perform Multiplication: Perform the multiplication. $(d)/(dx)[g(x)*h(x)]$ at $x=5$ = $-10 + 7$ .
Add Results: Add the results to get the final answer. $\newline$ $\frac{d}{dx}[g(x)\cdot h(x)]$ at $x=5$ = $-3$ .

More problems from Power rule

Question

h(x)=\log _{2}(x)

\newline

Can we use the mean value theorem to say the equation

h^{\prime}(x)=1

has a solution where

1<x<2

\newline

1

\newline

(A) No, since the function is not differentiable on that interval.

\newline

(B) No, since the average rate of change of

h

over the interval

1 \leq x \leq 2

1

\newline

(C) Yes, both conditions for using the mean value theorem have been met.

Posted 3 months ago

Question

What is the sign of

39 \frac{11}{13}+\left(-41 \frac{1}{13}\right) \text { ? }

\newline

1

\newline

\newline

\newline

(C) Neither positive nor negative-the sum is zero.

Posted 3 months ago

Question

What is the sign of

-1042+1042 ?

\newline

1

\newline

\newline

\newline

(C) Neither positive nor negative-the sum is zero.

Posted 3 months ago

Question

What is the sign of

-18 \frac{9}{17}+\left(-18 \frac{9}{17}\right)

\newline

1

\newline

\newline

\newline

(C) Neither positive nor negative-the sum is zero.

Posted 3 months ago

Question

What is the sign of

\frac{23}{45}+\left(-\frac{23}{45}\right) ?

\newline

1

\newline

\newline

\newline

(C) Neither positive nor negative-the sum is zero.

Posted 3 months ago

Question

What is the sign of

45+(-38)

\newline

1

\newline

\newline

\newline

(C) Neither positive nor negative-the sum is zero.

Posted 3 months ago

Question

What is the sign of

-49.8+61.2

\newline

1

\newline

\newline

\newline

(C) Neither positive nor negative-the sum is zero.

Posted 3 months ago

Question

What is the sign of

-1.69+(-1.69) ?

\newline

1

\newline

\newline

\newline

(C) Neither positive nor negative-the sum is zero.

Posted 3 months ago

Question

What is the sign of

37+(-37)

\newline

1

\newline

\newline

\newline

(C) Neither positive nor negative-the sum is zero.

Posted 3 months ago

Question

\begin{array}{l} g(x)=\sqrt{2 x-9} \\ g^{\prime}(x)=? \end{array}

\newline

1

\newline

\frac{\sqrt{2 x-9}}{2}

\newline

\frac{1}{\sqrt{2 x-9}}

\newline

\frac{1}{2 \sqrt{2 x-9}}

\newline

\frac{1}{\sqrt{x}}

Posted 3 months ago