**Problem : **
Find *f'*(*x*) for *f* (*x*) = 3*x*^{2} + sin(*x*)

**Problem : **
Find *f'*(*x*) for *f* (*x*) = - 4

x^{} = |

**Problem : **
Find *f'*(*x*) for *f* (*x*) =

= | |||

= |

**Problem : **
Find *f'*(*x*) for *f* (*x*) = cos(*x*^{2}).

-2

**Problem : **
Find *f'*(*x*) for *f* (*x*) = cos^{2}(*x*^{3}).

Since this is actually a composite of three functions, the chain rule has to be used twice:

(2 cos(x^{3}))(- sin(x^{3}))(3x^{2}) = - 6x^{2}cos(x^{3})sin(x^{3}) |

**Problem : **
Find the slope of the graph of 4*x*^{2}*y* = 2*y* + *x* at the point (0,0).

Here, implicit differentiation must be used.

42xy + x^{2} | = 2 + 1 | ||

8xy - 1 | = (2 - 4x^{2}) | ||

= | |||

At (x, y) | = (0, 0), | ||

= - |

Take a Study Break!