Best solutions to - "(a) Find the differential dyy=rad(15+x2) (b) Evaluate dy..."

petrusrexcs Answered2021-12-30

(a) Find the differential

d y y = r a d (15 + x 2)

(b) Evaluate dy for the given values of x and dx. x = 1, dx = −0.2

Answer & Explanation

Linda Birchfield

Expert

2021-12-31Added 39 answers

a). Given,

y = \sqrt{15 + x^{2}}

The differential of y is the derivative of the function times the differential of x.
Therefore,

d y = \frac{1}{2 \sqrt{15 + x^{2}}} \cdot \frac{d}{d x} (15 + x^{2}) \cdot d x

\Rightarrow d y = \frac{1}{2 \sqrt{15 + x^{2}}} \cdot (0 + 2 x) d x

d y = \frac{x}{\sqrt{15 + x^{2}}} d x

lalilulelo2k3eq

Expert

2022-01-01Added 38 answers

b). Substituting x=1 and dx=-0.2 in dy, we get

\Rightarrow d y = \frac{1}{\sqrt{15 + {(1)}^{2}}} c d o (- 0.2)

\Rightarrow d y = \frac{1}{\sqrt{16}} (- 0.2)

\Rightarrow d y = \frac{- 0.2}{4}

\Rightarrow d y = - 0.05

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