Find the derivative of \$ y = (x^2 + 1) sinx \$.

A) \$ (2x^2 + 1) cos(x) + 2x sin(x) \$

B) \$ (x^2 + 1) cos(x) + 2x sin(x) \$

C) \$ (2x^2 + 1) cos(x) + 3x sin(x) \$

D) \$ (x^2 + 1) cos(x) + 4x sin(x) \$

Find the derivative of \$ y = x^x \$.

A) \$ 2x^x (ln(x) + 1) \$

B) \$ x^x (ln(x) + 3) \$

C) \$ x^x (ln(x) + 1) \$

D) \$ 2x^x (ln(x) + 4) \$

Find \$ (d/dx)​(x^2sin(x^3)) \$.

A) \$ xsin(x^3) + 3x^4cos(x^3) \$

B) \$ 2xsin(x^3) + x^4cos(x^3) \$

C) \$ 4xsin(x^3) + 2x^4cos(x^3) \$

D) \$ 2xsin(x^3) + 3x^4cos(x^3) \$

Find the equation of the tangent line to the curve \$ g(x) = 4sin(2x) \$ at \$ x = (5π)/6 \$.

A) \$ y = 4x − ((10π)/3) ​+ 2\sqrt(3) \$​

B) \$ y = 2x − ((10π)/3) ​+ 2\sqrt(3) \$​

C) \$ y = 4x − ((7π)/3) ​+ 2\sqrt(3) \$​

D) \$ y = 2x − ((10π)/3) ​+ 2\sqrt(5) \$​

Compute the derivative of the given function. \$ p(x) = 2x + 3/(5x - 4) \$.

A) \$ −23/(5x − 4)^2​ \$

B) \$ −13/(2x − 4)^2​ \$

C) \$ −23/(5x − 2)^2​ \$

D) \$ −13/(5x − 4)^2​ \$

Given the function y defined implicitly by the equation: \$(x^2y + e^xy) = sin(x + y)\$ find \$dy / dx\$ at the point where x = 0 and y = 0.

A) -1

B) 1

C) 2

D) -3

Find the derivative of \$f(t) = 4 / t - 1 / 6t^3 + 8 / t^5\$.

A) \$f(t) = (-4t^-2) + (1 / 2t^-4) - (40t^-6)\$

B) \$f(t) = (-4t^-3) + (1 / 2t^-4) + (40t^6)\$

C) \$f(t) = (-3t^-2) - (1 / 3t^-4) - (40t^-6)\$

D) \$f(t) = (-4t^-2) + (1 / 2t^-4) - (45t^6)\$

Find the derivative of
\$R(z) = (6 / (sqrtz^3)) + (1 / (8z^4)) - (1 / (3z^10))\$.

A) \$-9z^-(5/2) - (1/ 2)z^-5 - (10/3)z^-15\$

B) \$-9z^-(5/2) - (1/ 2)z^-5 + (10/3)z^-11\$

C) \$-10z^-(5/2) + (1/ 2)z^-5 + (10/3)z^-11\$

D) \$-9z^-(5/2) - (1/ 5)z^-5 + (10/3)z^-11\$

Find the derivative of \$z = x (3x^2 - 9)\$.

A) \$dz / dx = 9x^2 + 10\$

B) \$dz / dx = 9x^3 - 9\$

C) \$dz / dx = 9x^2 - 9\$

D) \$dz / dx = 9x^2 - 12\$

Find the derivative of \$g(y) = (y - 4) (2y + y^2)\$.

A) \$g(y) = 3y^2 - 5y - 9\$

B) \$g(y) = 3y^3 + 4y - 8\$

C) \$g(y) = 3y^2 - 5y - 10\$

D) \$g(y) = 3y^2 - 4y - 8\$