Derivatives

Find the derivative of f(x) = x²sinx

• f'(x) = 2xsinx - x²cosx
• f'(x) = 2xsinx + x²sinx
• f'(x) = 2xsinx + x²cosx
• f'(x) = 2xcosx

Quotient Rule with respect to the derivative.  f/g

• (gf'-fg')/g^2
• (gf'+fg')/g^2
• (fg'-gf')/f^2

Set up the derivative of y=(3x⁴ - 7)*(5x² + 1)

• (12x³)*(10x)
• (3x⁴ - 7)*(10x) + (12x³)*(5x² + 1)
• (3x⁴ - 7)*(10x) - (12x³)*(5x² + 1)
• (3x⁴ - 7)/(10x) + (12x³)/(5x² + 1)

Which of the following is the product rule for derivatives utilizing the original function h(x) = f(x)g(x) ?

• h^'(x)= f^'(x)g^'(x)

• h^'(x)=f^'(x)g^'(x) + f(x)g(x)

• h^'(x)=f^'(x)g(x) - f(x)g^'(x)

• h^'(x)=f^'(x)g(x) + f(x)g^'(x)

Which of the following is the quotient rule for derivatives?

• h^'(x)=((g(x)f^'(x) + f(x)g^'(x)) / (g(x))²

• h^'(x)=((g^'(x)f^'(x) - f(x)g(x)) / (g(x))

• h^'(x)=((g(x)f^'(x) - f(x)g^'(x)) / (g(x))²

• h^'(x)=((g^'(x)f^'(x) + f(x)g(x)) / (g(x))