+0  
 
0
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avatar+821 

If f(4) = -8, f'(4) = 3, g(4) = 3pi, and g'(4) = 4

 

and h(x)= 5 f(x)- 2/3 g(x)

 

find h'(x).

 Sep 26, 2018

Best Answer 

 #2
avatar+7348 
+3

\(h(x)\,=\,5f(x)-\frac23g(x)\\~\\ \frac{d}{dx}[h(x)]\,=\,\frac{d}{dx}[5f(x)-\frac23g(x)]\\~\\ \frac{d}{dx}[h(x)]\,=\,\frac{d}{dx}[5f(x)]-\frac{d}{dx}[\frac23g(x)]\\~\\ \frac{d}{dx}[h(x)]\,=\,5\frac{d}{dx}[f(x)]-\frac23\frac{d}{dx}[g(x)]\\~\\ h'(x)\,=\,5f'(x)-\frac23g'(x)\)

 

That is the most you can say I think. smiley

 Sep 27, 2018
 #1
avatar+97586 
+2

Landry, are you sure this question is written properly?   frown

 Sep 27, 2018
 #2
avatar+7348 
+3
Best Answer

\(h(x)\,=\,5f(x)-\frac23g(x)\\~\\ \frac{d}{dx}[h(x)]\,=\,\frac{d}{dx}[5f(x)-\frac23g(x)]\\~\\ \frac{d}{dx}[h(x)]\,=\,\frac{d}{dx}[5f(x)]-\frac{d}{dx}[\frac23g(x)]\\~\\ \frac{d}{dx}[h(x)]\,=\,5\frac{d}{dx}[f(x)]-\frac23\frac{d}{dx}[g(x)]\\~\\ h'(x)\,=\,5f'(x)-\frac23g'(x)\)

 

That is the most you can say I think. smiley

hectictar Sep 27, 2018
 #3
avatar+821 
+2

I eventually got the answer. 

h(x)=5f(x)−23g(x)

 

d/dx[h(x)]=d/dx[5f(x)−23g(x)]

 

h ′(x)=d/dx[5f(x)]−d/dx[23g(x)]

 

h ′(x)=5d/dx[f(x)]−23d/dx[g(x)]

 

h ′(x)=5f ′(x)−23g ′(x)

 

h ′(4)=5f ′(4)−23g ′(4)

 

h ′(4)=5∗3−23∗4

 

h ′(4)=15−83

 

h ′(4)=453−83

 

h ′(4)=45−83

 

h ′(4)=373

 Sep 27, 2018

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