What is the derivative of ln(2*2^{2x+3}) ?

The derivative of ln(2*2^{2x+3}) is ln^2(2)*2^{2x+4}

What is the first derivative of ln(2*2^{2x+3}) ?

The first derivative of ln(2*2^{2x+3}) is ln^2(2)*2^{2x+4}

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

ln^{2} (2) \cdot 2^{2 x + 4}

Solution steps

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply exponent rule:

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

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

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

Apply the chain rule:

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

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

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

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

Simplify

ln (2) e^{(2 x + 3) l n (2)} \cdot 2 ln (2) : ln^{2} (2) \cdot 2^{2 x + 4}

= ln^{2} (2) \cdot 2^{2 x + 4}

\frac{\partial}{\partial x} (x y + 3 y)

x \to 2 lim (- x^{2} + b x - 1)

\frac{d}{d x} (4 x^{2} - 11 x - \frac{5}{x ^{3}})

x \to 0 lim (cos (4 x))

(x^{2} + 1) y^{^{'}} + 4 x (y - 1) = 0

What is the derivative of ln(2*2^{2x+3}) ?
The derivative of ln(2*2^{2x+3}) is ln^2(2)*2^{2x+4}
What is the first derivative of ln(2*2^{2x+3}) ?
The first derivative of ln(2*2^{2x+3}) is ln^2(2)*2^{2x+4}