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Calculus 1: Product and Quotient Rule

Use the product rule to find the derivative of

f(x)=(x3+5x)(2x2)f(x) = (x^3 + 5x)(2x^2)

Find the derivative of f(x)=sinx(x2+5)f(x) = \sin{x}(x^2 + 5)

Use the product rule to find the derivative of y=5x(x22)y = 5x(x^2 - 2)

Use the product rule to find the derivative of y=(3x2+2x)(2x45)y = (3x^2 + 2x) (2x^4 - 5)

Find the first derivative of y=2xsin(x2)y = 2x \sin({x^2})

Find the derivative of y=e2x(x1)+85x2y = e^{2x}(x-1) + 8 - 5x^2

Use the quotient rule to find the derivative of the following funciton,

f(x)=x1x2+2x+1f(x) = \frac{x - 1}{x^2 + 2x + 1}

Find f(x)f\prime(x)

f(x)=5x212x3+3f(x) = \frac{5x^2 - 1}{2x^3 + 3}

Given f(x)f(x), find the equation of the tangent line at the point (1,2)(-1, -2)

f(x)=4x(1+x2)f(x) = \frac{4x}{(1 + x^2)}

Use the quotient rule to find the derivative of y=5x6x2+2xy = \frac{5x}{6x^2 + 2x}