Differentiation

Find $f^{\text{'}}(x)$ if $f(x)=\frac{5}{3}{x}^6-\frac{2}{5}{x}^{\frac{3}{2}}+2x^2-153$

Find $y^{\text{'}}$ if $y=3x^2\sqrt[\phantom{2}]{4-2x}$

Find $f^{\text{'}}(x)$ if $f(x)=\frac{\sqrt[3]{x^2-5}}{x^2+5}$

Find $g^{\text{'}}()$ if $g()=3sin(5)-5tan(3)$

Find $\frac{dy}{(d)x}$ if $y=co{s}^2(x)+ta{n}^{-1}(x)$

Implicit Differentiation

Find $\frac{dy}{dx}$ by implicit differentiation.

$6.x^3+y^3=1$

$7.4cos(x)sin(y)=1$

$8.e^{y}cos(x)=1+sin(xy)$

$9.tan(x-y)=\frac{y}{1+x^2}$

Indefinite Integrals $($Antiderivatives$)$

$10.{\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}\frac{1}{2}{x}^2-2x+6dx$

$13.{\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}{x}^2(x^3+5{)}^{9}dx$

$11.{\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}5x^{\frac{1}{4}}-13x^{\frac{3}{4}}dx$

$14.{\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}\frac{cos(\sqrt[\phantom{2}]{t})}{\sqrt[\phantom{2}]{t}}dt$

$12.{\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}cos()-5sin()d$

$15.{\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}{e}^{tan(x)}se{c}^2(x)dx$

Definite Integrals and the Fundamental Theorem of Calculus $($FTC$)$

$16.{\displaystyle \underset{-1}{\overset{2}{}}}{x}^3-2xdx$

$19.{\displaystyle \underset{7}{\overset{0}{}}}\sqrt[\phantom{2}]{4+3x}dx$

$17.{\displaystyle \underset{0}{\overset{\frac{}{4}}{}}}sec()tan()d$

$20.{\displaystyle \underset{1}{\overset{2}{}}}\frac{e^{\frac{1}{x}}}{x^2}dx$

$18.{\displaystyle \underset{0}{\overset{1}{}}}\frac{4}{1+t^2}dt$

$21.{\displaystyle \underset{0}{\overset{\frac{}{2}}{}}}cos(x)sin(sin(x))dx$