Find the derivative.

a$.f^{\text{'}}(x)$ for $f(x)=x^6$

b$.\frac{dy}{dx}$ for $y=\frac{1}{x^4}$

c$.\frac{d}{dx}\sqrt[\phantom{2}]{x}$

Find the derivative $f^{\text{'}}(x)$ for each function $f(x).$

a$.f(x)=4x^4-3x^{3}2x^2-7x5$

b$.f(x)=x^{\frac{7}{3}}3\sqrt[4]{x^3}-\frac{2}{x^{\frac{2}{5}}}$

c$.f(x)=\frac{4x^3-9x}{x^2}$

Let $f(x)=3x^4-6x^2-7$

a$.$ Find $f^{\text{'}}(x).$

b$.$ Find the slope of the graph of $y=f(x)$ at $x=2.$

c$.$ Find the equation of the tangent line at $x=2.$

d$.$ Find the values of $x$ where the tangent line is horizontal.