Practice section 5 of 8

Differentiate $(3x^2+1)(2x+7)$ with respect to $x$ using the product rule.

Differentiate $\dfrac{2x^3+3}{x^4+2}$ with respect to $x$.

Differentiate $\sqrt{3x-2}$ with respect to $x$.

Differentiate with respect to $x$: (a) $4e^{2x+1}$; (b) $x^2\sin x$; (c) $\ln(3x)$.

Integrate the following expressions with respect to $x$: (a) $2x^2+3x+1$; (b) $(5x+4)^5$; (c) $2e^{2x-1}$; (d) $\sin(2-3x)$.

Given that $\dfrac{10+v}{10-v}=Ae^t$, express $v$ in terms of $A$ and $t$.