Mathematics, 17.11.2020 04:00 randyg0531

Find the Derivative.
f(x) = -xcos3x

Answers: 2

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Answer from: maskythegamer

$\frac{d}{dx}(-xcos3x)= 3x \ sin(3x)- cos(3x)$

Step-by-step explanation:

Use the Product Rule for derivatives, which states that:

$\frac{d}{dx} =[f(x)g(x)]= f(x)g'(x)+f'(x)g(x)$

In the function we are given, $f(x)=-x \cos3x$ , we can break it up into two factors: -x is being multiplied by cos3x.

Now, we have the factors:

$-x \\ $cos 3x$

Before using the product rule, let's find the derivative of cos3x using the chain rule and the power rule.

$\frac{d}{dx}(cos3x)= \frac{d}{dx} (cos3x) \times \frac{d}{dx} (3x) \\ \frac{d}{dx}(cos3x)= (-sin3x) \times 3 \\ \frac{d}{dx} (cos3x) = -3sin(3x)$

Now let's apply the product rule to f(x) = -xcos3x.

$\frac{d}{dx}(-xcos3x)= (-x)(-3sin3x) + (-1)(cos3x)$

Simplify this equation.

$\frac{d}{dx}(-xcos3x)= (x)(3sin3x) - (cos3x)$

Multiply x and 3 together and remove the parentheses.

$\frac{d}{dx}(-xcos3x)= 3x \ sin(3x)- cos(3x)$

Therefore, this is the derivative of the function f(x)=-xcos3x .

Answer from: aredding6282

Hi there!

$\large\boxed{f'(x) = -cos3x + 3xsin3x}$

$f(x) = -xcox3x\\\\\text{Use the product rule and chain rule to solve for the derivative:}\\\\\frac{dy}{dx}= -cos3x + (-x * (-sin3x) * 3)\\\\= -cos3x + 3xsin3x$

Answer from: Quest

(x3 + 6x2 + 2x - 6) • (x - 1)

step-by-step explanation:

polynomial long division :

3.2 polynomial long division

dividing : x4+5x3-4x2-8x+6

("dividend")

by : x-1 ("divisor")

dividend x4 + 5x3 - 4x2 - 8x + 6

- divisor * x3 x4 - x3

remainder 6x3 - 4x2 - 8x + 6

- divisor * 6x2 6x3 - 6x2

remainder 2x2 - 8x + 6

- divisor * 2x1 2x2 - 2x

remainder - 6x + 6

- divisor * -6x0 - 6x + 6

remainder 0

quotient : x3+6x2+2x-6 remainder: 0

Answer from: Quest

option 3 . (5x + 1) - (-10x + 6)

step-by-step explanation:

option 1 :

(4x + 3) + (-9x + 4)

or 4x+3 -9x + 4

or -5x + 7

option 2

(x - 2) - (6x - 9)

or x-2-6x + 9

or -5x + 7

option 3

(5x+ + 6)

or 5x + 1 + 10x -6

or 15x -5

option 4

-4x+2x+7-3x

-7x + 2x + 7

-5x + 7

hence only option 3 did not satisfy the given simplify expression.

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f(x) = -xcos3x...

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