What is the derivative of (3x+2^x) ?

The derivative of (3x+2^x) is (ln(3x+2)+(3x)/(3x+2))(3x+2)^x

What is the first derivative of (3x+2^x) ?

The first derivative of (3x+2^x) is (ln(3x+2)+(3x)/(3x+2))(3x+2)^x

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\frac{d}{d x} ((3 x + 2)^{x})

(ln (3 x + 2) + \frac{3 x}{3 x + 2}) (3 x + 2)^{x}

Solution steps

\frac{d}{d x} ((3 x + 2)^{x})

Apply exponent rule:

a^{b} = e^{b l n (a)}

(3 x + 2)^{x} = e^{x l n (3 x + 2)}

= \frac{d}{d x} (e^{x l n (3 x + 2)})

Apply the chain rule:

e^{x l n (3 x + 2)} \frac{d}{d x} (x ln (3 x + 2))

= e^{x l n (3 x + 2)} \frac{d}{d x} (x ln (3 x + 2))

\frac{d}{d x} (x ln (3 x + 2)) = ln (3 x + 2) + \frac{3 x}{3 x + 2}

= e^{x l n (3 x + 2)} (ln (3 x + 2) + \frac{3 x}{3 x + 2})

e^{x l n (3 x + 2)} = (3 x + 2)^{x}

= (ln (3 x + 2) + \frac{3 x}{3 x + 2}) (3 x + 2)^{x}

y^{^{''}} + y^{^{'}} + 4 y = 0

6 x sin (x)

\frac{\partial}{\partial y} (x^{\frac{x}{y}} cos (\frac{x}{y}))

((4 - x^{\frac{2}{3}})^{\frac{3}{2}})^{^{'}}

f (x) = \frac{1 + 2 x}{3 + x}

What is the derivative of (3x+2^x) ?
The derivative of (3x+2^x) is (ln(3x+2)+(3x)/(3x+2))(3x+2)^x
What is the first derivative of (3x+2^x) ?
The first derivative of (3x+2^x) is (ln(3x+2)+(3x)/(3x+2))(3x+2)^x