Calculus 1

$\int \frac{6}{\sqrt{x-9x^2}}\ dx$

Let $g(x) = \frac{|x^2 + x - 6|}{x - 2}$

Find the limit as $x\rightarrow 2^{+} x\rightarrow 2^{-} x\rightarrow 2$

$\lim_{x\rightarrow \infty}(\frac{5}{x} - \arctan{x})$

$\lim_{x\rightarrow -\infty} \frac{x}{\sqrt{x^2 + 1}}$

$\lim_{x\rightarrow 0} \frac{\sin{(3x)}}{x}$

Find the derivative of the following function using the limit definition of derivative,

$f(x) = 8x + 4$

Find the slope of the tangent line to

$f(x) = \sqrt{x}$

when x = 1

Use the product rule to find the derivative of

$f(x) = (x^3 + 5x)(2x^2)$

Find the derivative of $y = 2x^2 + 3x - 17$

Find the derivative of $f(x) = x$

Find the derivative of $f(x) = \frac{1}{x^2}$

Find the derivative of $f(x) = -12x^{0.25}$

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

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

Find $f\prime(x)$

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

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

Use the quotient rule to find the derivative of $\sec{x}$

What is the derivative of $y = x{}\cos{(x)}$

Find the derivative of $f(x) = x^{3}e^{-2x}$

Find the derivative of $h(x) = 8^{x}\log_{9}x$