What is the derivative of 3*2^{2x+1} ?

The derivative of 3*2^{2x+1} is 3ln(2)*2^{2x+2}

What is the first derivative of 3*2^{2x+1} ?

The first derivative of 3*2^{2x+1} is 3ln(2)*2^{2x+2}

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derivative of

3 \cdot 2^{2 x + 1}

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

Solution steps

\frac{d}{d x} (3 \cdot 2^{2 x + 1})

Take the constant out:

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

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

Apply exponent rule:

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

2^{2 x + 1} = e^{(2 x + 1) l n (2)}

= 3 \frac{d}{d x} (e^{(2 x + 1) l n (2)})

Apply the chain rule:

e^{(2 x + 1) l n (2)} \frac{d}{d x} ((2 x + 1) ln (2))

= e^{(2 x + 1) l n (2)} \frac{d}{d x} ((2 x + 1) ln (2))

\frac{d}{d x} ((2 x + 1) ln (2)) = 2 ln (2)

= 3 e^{(2 x + 1) l n (2)} \cdot 2 ln (2)

Simplify

3 e^{(2 x + 1) l n (2)} \cdot 2 ln (2) : 3 ln (2) \cdot 2^{2 x + 2}

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

\int_{0}^{1} r 1 - r^{2} d r

\int (\frac{x ^{3}}{x - 1}) d x

\frac{d}{d x} ((1 - x)^{3} - 3 x (1 - x)^{2})

\frac{d y}{d x} = \frac{x - 1}{3 x ^{2} - 6 x - 1}

\int (ln (x)) 2 d x

What is the derivative of 3*2^{2x+1} ?
The derivative of 3*2^{2x+1} is 3ln(2)*2^{2x+2}
What is the first derivative of 3*2^{2x+1} ?
The first derivative of 3*2^{2x+1} is 3ln(2)*2^{2x+2}