APFIVE Derivative of a Composite Function
Differentiate $$y=\left(\sum_{j=1}^{3}\sqrt{j*x+1}\right)^{2}$$ with respect to x.
TITLE: Table of Summation Terms: #000000
| j | Expression |
|---|---|
| 1 | \sqrt{1*x+1} |
| 2 | \sqrt{2*x+1} |
| 3 | \sqrt{3*x+1} |
A
$$y'=\left(\sqrt{x+1}+\sqrt{2*x+1}+\sqrt{3*x+1}\right)\left(\frac{1}{\sqrt{x+1}}+\frac{2}{\sqrt{2*x+1}}+\frac{3}{\sqrt{3*x+1}}\right)$$
B
$$y'=\frac{\sqrt{x+1}+\sqrt{2*x+1}+\sqrt{3*x+1}}{\frac{1}{\sqrt{x+1}}+\frac{2}{\sqrt{2*x+1}}+\frac{3}{\sqrt{3*x+1}}}$$
C
$$y'=2*\left(\sqrt{x+1}+\sqrt{2*x+1}+\sqrt{3*x+1}\right)\left(\frac{1}{\sqrt{x+1}}+\frac{2}{\sqrt{2*x+1}}+\frac{3}{\sqrt{3*x+1}}\right)$$
D
$$y'=\left(\sqrt{x+1}+\sqrt{2*x+1}+\sqrt{3*x+1}\right)^{2}\left(\frac{1}{\sqrt{x+1}}+\frac{2}{\sqrt{2*x+1}}+\frac{3}{\sqrt{3*x+1}}\right)$$
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