Evaluate the following derivatives.

$\frac{d}{dx}{\int}_{7}^{x}\sqrt{1+{t}^{4}+{t}^{6}}dt$

Wierzycaz
2021-02-22
Answered

Evaluate the following derivatives.

$\frac{d}{dx}{\int}_{7}^{x}\sqrt{1+{t}^{4}+{t}^{6}}dt$

You can still ask an expert for help

Macsen Nixon

Answered 2021-02-24
Author has **117** answers

Step 1

Formula

$\frac{d}{dx}{\int}_{a\left(x\right)}^{b\left(x\right)}f(x,t)dt={\int}_{a\left(x\right)}^{b\left(x\right)}\frac{\partial}{\partial x}(f(x,t)dt+{b}^{\prime}\left(x\right)f(x,b)-{a}^{\prime}\left(x\right)f(x,a)$

Step 2

By formula

$\frac{d}{dx}{\int}_{7}^{x}\sqrt{1+{t}^{4}+{t}^{6}}dt=\left({\int}_{7}^{x}0\right)+\sqrt{1+{x}^{4}+{x}^{6}}-0=\sqrt{1+{x}^{4}+{x}^{6}}$

Formula

Step 2

By formula

asked 2021-05-23

Use the given graph to estimate the value of each derivative.(Round all answers to one decimal place.)Graph uploaded below.

(a) f ' (0)1

(b) f ' (1)2

(c) f ' (2)3

(d) f ' (3)4

(e) f ' (4)5

(f) f ' (5)6

(a) f ' (0)1

(b) f ' (1)2

(c) f ' (2)3

(d) f ' (3)4

(e) f ' (4)5

(f) f ' (5)6

asked 2021-03-07

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? Give examples.

asked 2021-05-23

Find the derivatives of the functions.

asked 2021-12-07

Find the derivatives of the functions

$y=(1+{x}^{2}){e}^{{\mathrm{tan}}^{-1}x}$

asked 2021-10-14

Calculating derivatives Find dy>dx for the following functions.

$y=\frac{1-\mathrm{cos}x}{1+\mathrm{cos}x}$

asked 2021-10-18

Solve the derivatives of the following functions.

$f\left(x\right)=10{x}^{8}-4{x}^{5}+2{x}^{3}-18x-9$

asked 2021-10-20

Find the derivatives of the functions

$z=\frac{4-3x}{3{x}^{2}+x}$