Answer:
Step-by-step explanation:
We know the property of derivative: ![\dfrac{d}{dx}(\log (x))=\dfrac{1}{x}](https://tex.z-dn.net/?f=%5Cdfrac%7Bd%7D%7Bdx%7D%28%5Clog%20%28x%29%29%3D%5Cdfrac%7B1%7D%7Bx%7D)
Given function : ![y=\ln(3 + x^2)](https://tex.z-dn.net/?f=y%3D%5Cln%283%20%2B%20x%5E2%29)
Differentiate both sides with respect to x , we get
![\dfrac{dy}{dx}=\dfrac{d}{dx}(\ln(3 + x^2))](https://tex.z-dn.net/?f=%5Cdfrac%7Bdy%7D%7Bdx%7D%3D%5Cdfrac%7Bd%7D%7Bdx%7D%28%5Cln%283%20%2B%20x%5E2%29%29)
[By Chain rule]
![\Rightarrow\ \dfrac{dy}{dx}=\dfrac{1}{3 + x^2}\cdot(0+2x)](https://tex.z-dn.net/?f=%5CRightarrow%5C%20%5Cdfrac%7Bdy%7D%7Bdx%7D%3D%5Cdfrac%7B1%7D%7B3%20%2B%20x%5E2%7D%5Ccdot%280%2B2x%29)
[Since
, where a is scalar and
]
![\Rightarrow\ \dfrac{dy}{dx}=\dfrac{2x}{3 + x^2}](https://tex.z-dn.net/?f=%5CRightarrow%5C%20%5Cdfrac%7Bdy%7D%7Bdx%7D%3D%5Cdfrac%7B2x%7D%7B3%20%2B%20x%5E2%7D)
Hence, the derivative of the given function is
.
Answer:
5.8 m
Step-by-step explanation:
From the diagram given :
XY = opposite angle the angle. of depression = 30
To obtain the height YZ ;apply the trigonometric relation :
Tan θ = opposite / Adjacent
Tan 30° = YZ / 10
YZ = 10 * tan 30
YZ = 10 * 0.5773502
YZ = 5.77 m
The height is about 5.8 m
Answer:
20%
Step-by-step explanation:
3 + 4 + 3 + 5 + 1 + 3 + 6=25
She has 5 pink socks so 5/25 as a percent is 20%
Answer:
The slope of a vertical line is <u>undefined</u>
The slope of a horizontal line is <u>zero</u>