Mathematics - Pre-calculus 20 - Multiplication of derivatives

Pre-calculus 20 - Multiplication of derivatives

(10 Questions)

3 viewed last edited 6 years ago

Mathematics

These questions will introduce the product rule for calculating the derivatives.

\frac{d}{dx} (x^2+1)(x^2+1) =_____

4x^3+4x

2x(x^2+1)

4 x(x^2+1)

-2x(x^2+1)

[math]\frac{d}{dx} [p(x)*q(x)+r(x)]=p(x)g'(x)+p'(x)q(x)+r'(x)[/math]

True

False

Find the derivative of y = x^sin x

y' = x^{sin x}(cos x) ln x + \frac{(cos x)}{x}

y' = x(cos x) + \frac{(sin x)}{x}

y' = x^{sin x} (cos x) ln x + \frac{(sin x)}{x}

y' = x^{cos x} (cos x) ln x + \frac{(sin x)}{x}

[math] \frac{d}{dx} [\log x \sin x] [/math] =______.

\frac{sin x}{ x}+ x cos x

\frac{sin x}{ x}+\log x sin x

\frac{1}{ sin x}+\log x cos x

\frac{sin x}{ x}+\log x cos x

Find the derivative of y= x^2 sin^3 (2x)

[math] xsin^2 (2x)[2sin (2x)+6] [/math]

[math] xsin^2 (2x)[2sin (2x)+6x] [/math]

[math] sin^2 (2x)[2sin (x)+6x] [/math]

[math] xsin (2x)[2sin (2x)+6x] [/math]

Find the derivative of y=x^2(3x+1)

9x^2 + 2x

x^2 + 2x

9x^2 + x

9x^2 + 2

Differentiate the following function. f(x)=(3x^2-x)(7-10x)

-30x^2+62x-7

-90x^2+22x-7

-30x^2+62x+7

-90x^2+62x-7

Find \frac{d}{dx}h(x), h(x)=x^2 sin x.

2 sin x + x^2cosx

x^2 sin x + x^2cosx

2x sin x + x^2cosx

2x sin x + 2xcosx

Find the derivative of y=9xe^x

[math] e^x[1+x][/math]

[math] 9e^x[1-x][/math]

[math] 9[1+x][/math]

[math] 9e^x[1+x][/math]

Look at the attachment above and find the y' for y=cos (x) sin (x)

-sin^2 x

cos^2 (x) +sin^2 (x)

cos^2 (x)- sin^2 (x)

by Krishna (Expert, Educator @Qalaxia)