PRAXIS: Derivative Rules

Find the derivative of the following functions

1. \(f(x)=4x^2+4x+1\)
2. \(g(x)=5e^x+3.14x+\ln(x)\)
3. \(h(t)=(t^2+1)^4\)
4. \(f(r)=(3r^2-5r+1)\cdot e^r\)
5. \(k(x)=e^x\cdot \ln(x)\)
6. \(J(t)=\frac{t^2}{t^2-6t+1}\)
7. \(L(p)=\ln(x^{30}+e^x)\)
8. \(P(t)=e^{x^3-2x}\)
9. \(T(x)=\frac{x^7+\ln(x)}{x+1}\)
10. \(N(x)=\frac{\ln(x^2+5)}{x^2-1}\)
11. \(P(t)=(x^2+1)^5\cdot (x^3-2x+1)^3\)

Find the instantaneous rate of change of each of the following functions at the given \(x\)-value.

12. \(G(x)=x^2+5.142x+9.6\) at \(x=1.45\)
13. \(H(x)=(4x^2+1)^5\cdot (x^2-1)\) at \(x=2\)
14. \(K(x)=\frac{e^{4x}}{7x+1}\) at \(x=0\)

Find the equation of the line tangent to the function at the given \(x\)-value:

15. \(f(x)=x^2+5x+3\) at \(x=1\)
16. \(g(x)=(5x^2+6x+7)^3\) at \(x=0\)
17. \(h(x)=\frac{5}{x^3}\) at \(x=1\)