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# Calc

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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).

Landry  Sep 26, 2018

#2
+7339
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$$h(x)\,=\,5f(x)-\frac23g(x)\\~\\ \frac{d}{dx}[h(x)]\,=\,\frac{d}{dx}[5f(x)-\frac23g(x)]\\~\\ \frac{d}{dx}[h(x)]\,=\,\frac{d}{dx}[5f(x)]-\frac{d}{dx}[\frac23g(x)]\\~\\ \frac{d}{dx}[h(x)]\,=\,5\frac{d}{dx}[f(x)]-\frac23\frac{d}{dx}[g(x)]\\~\\ h'(x)\,=\,5f'(x)-\frac23g'(x)$$

That is the most you can say I think.

hectictar  Sep 27, 2018
#1
+94100
+2

Landry, are you sure this question is written properly?

Melody  Sep 27, 2018
#2
+7339
+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.

hectictar  Sep 27, 2018
#3
+820
+1

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

Landry  Sep 27, 2018