x_0=

b=

more options

c=

k=

k = 1
b = 2
c = 1
f(x) = (c * b^((k * x)))
fprime = Derivative(f)
A = Point(f)
x0 = 1
fprimex0: fprime(x0)
tanlin(x) = f(x0) + (fprimex0 * (x - x0))
inputBox1 = Textfield(x0)
inputBox2 = Textfield(b)
fx0: f(x0)
text1: "$ f(" + (LaTeX[x0]) + ")= " + (LaTeX[fx0]) + "$"
text2: "$ f'(" + (LaTeX[x0]) + ")=" + (LaTeX[fprimex0]) + " $"
fprimefx0: fprimex0 / fx0
text4: "$ \frac{f'( " + (LaTeX[x0]) + ")}{f( " + (LaTeX[x0]) + ")}=\frac{" + (LaTeX[fprimex0]) + " }{" + (LaTeX[fx0]) + " }=" + (LaTeX[fprimefx0]) + " $"
B = Point(fprime)
moreoptions = false
inputBox3 = Textfield(c)
inputBox4 = Textfield(k)
bwithe = SurdText(b, {2.7182818284590455})
ftext = If(c ≟ 1, If[k ≟ 1, bwithe + "^x", bwithe + "^{" + k + "x}"], If[k ≟ 1, c + "\cdot" + bwithe + "^x", c + "\cdot" + bwithe + "^{" + k + "x}"])
text10: "$f(x)=" + (LaTeX[ftext]) + "$"
ratio(x) = fprime(x) / fprime(x)