erurnSopSoypegx

2021-12-05

Use the rules for derivatives to find the derivative of function defined as follows.

$y=10\cdot {2}^{\sqrt{x}}$

Gloria Lusk

Beginner2021-12-06Added 18 answers

Step 1: Consider the given

Function,$y=10\cdot {2}^{\sqrt{x}}$

Step 2: The objective

Is to find the derivative of the function.

Step 3: Concept used

Since, we know,$\frac{d}{dx}\left({a}^{g\left(x\right)}\right)=\left(\mathrm{ln}a\right){a}^{g\left(x\right)}{g}^{\prime}\left(x\right)$

Thus, here we will let$g\left(x\right)=\sqrt{x}\Rightarrow {g}^{\prime}\left(x\right)=\frac{1}{2\sqrt{x}}$

Step 4: Calculation

Hence, the required derivatives is as follows,

$\frac{dy}{dx}=10\cdot \frac{d}{dx}\left({2}^{\sqrt{x}}\right)$

$=10\left(\mathrm{ln}2\right){2}^{\sqrt{x}}\left(\frac{1}{2\sqrt{x}}\right)$

$=\frac{5}{\sqrt{x}}\left(\mathrm{ln}2\right){2}^{\sqrt{x}}$

Function,

Step 2: The objective

Is to find the derivative of the function.

Step 3: Concept used

Since, we know,

Thus, here we will let

Step 4: Calculation

Hence, the required derivatives is as follows,

What is the Mixed Derivative Theorem for mixed second-order partial derivatives? How can it help in calculating partial derivatives of second and higher orders?

How do I find the y-intercept of a parabola?

What are the vertices of $9{x}^{2}+16{y}^{2}=144$?

How to determine the rate of change of a function?

Why are the tangents for 90 and 270 degrees undefined?

How to find the center and radius of the circle ${x}^{2}+{y}^{2}-6x+8y=0$?

What is multiplicative inverse of a number?

How to find the continuity of a function on a closed interval?

How do I find the tangent line of a function?

How to find vertical asymptotes using limits?

How to find the center and radius of the circle ${x}^{2}-12x+{y}^{2}+4y+15=0$?

Let f be a function so that (below). Which must be true?

I. f is continuous at x=2

II. f is differentiable at x=2

III. The derivative of f is continuous at x=2

(A) I (B) II (C) I and II (D) I and III (E) II and IIIHow to find the center and radius of the circle given ${x}^{2}+{y}^{2}+8x-6y=0$?

How to find the center and radius of the circle ${x}^{2}+{y}^{2}+4x-8y+4=0$?

How to identify the center and radius of the circle ${(x+3)}^{2}+{(y-8)}^{2}=16$?