Calculus Quiz 8. Ver 1. Chain Rule

Differentiate y = (x³ – 13)⁵ with respect to x

• 15x²(x³ – 13)⁴

• 5x²(x³ – 13)⁴

• 15(x³ – 13)⁴

• 5(3x²) 4

Find the derivative of f(𝒙) = (2𝒙² +6𝒙 + 5)³

• (4x + 6) ((2𝒙² +6𝒙 + 5)²

• (12x + 18) ((2𝒙² + 6𝒙 + 5 )²

• 3(2𝒙² + 6𝒙 + 5 )²

• 3(4x + 6)²

Differentiate  with  respect  to  x

 $f\left(x\right)=\frac{7}{3x+5}$  

•  $\frac{-21}{\left(3x+5\right)^2}$  

•  $\frac{21}{\left(3x+5\right)^2}$  

•  $\frac{7}{\left(3x+5\right)^2}$  

•  $\frac{-7}{3\left(3x+5\right)^2}$  

Find the Derivative of 

 $y=\left(-8x^2\ -\ 4\right)^{-2}\$  

• 
  

   $\frac{32x}{\left(-8x^2-4\right)^3}$ 

•  $\frac{-32x}{\left(-8x^2-4\right)^3}$ 

•  $\frac{-2}{\left(-8x^2-4\right)^{-3}}$ 

•  $\frac{32x}{\left(-8x^2-4\right)^1}$ 

Find the derivative of  f(x) = 4cos(7x)

• 28cos(7x)

• -4sin(7x)

• 28sin(7x)

• -28sin(7x)

Find the Derivative of   $f\left(x\right)=8\tan\left(\frac{3}{4}x\right)\$  

•  $\frac{3}{4}\sec^2\left(\frac{3}{4}x\right)$  

•  $6\tan\left(\frac{3}{4}x\right)$  

•  $6\sec^2\left(\frac{3}{4}x\right)\$  

•  $\frac{3}{4}\tan\left(\frac{3}{4}x\right)$  

Find the Derivative of   $\ y\ =\ \sqrt{\left(3x-7\right)^5}$  

•  $\frac{5}{2}\sqrt{\left(3x-7\right)^3}$  

•  $\frac{15}{2}\sqrt{\left(3x-7\right)^5}$  

•  $\frac{15}{2}\sqrt{\left(3x-7\right)^3}$  

•  $\frac{15}{6}\sqrt{\left(3x-7\right)^3}$  

Find the derivative of y = sin(3x) – cos(7x)

• cos(3x) + sin(7x)

• 3sin(3x) + 7cos(7x)

• 3cos(3x) – 7cos(7x)

• 3cos(3x) + 7sin(7x)

Different with respect to x   $\ y\ =2\sin\left(5x^3-1\right)$  

•  $30x^2\cos\left(5x^3-1\right)$  

•  $30x^2\sin\left(5x^3-1\right)$  

•  $-30x^2\cos\left(5x^3-1\right)$  

•  $15x^2\cos\left(5x^3-1\right)$  

•  $10x^3\cos\left(5x^3-1\right)$  

If  $y=-7\sin^3x\$ ,   what is   $\frac{\text{d}y}{\text{d}x}$  ?

•  $-21\sin^2\left(x\right)\cos\left(x\right)$  

•  $-21\cos^2\left(x\right)\sin\left(x\right)$  

•  $7\sin^2\left(x\right)\cos\left(x\right)$  

•  $21\sin^2\left(x\right)\cos\left(x\right)$  

•  $-21\cos^3x$