What is the derivative of 2^{3x+1}ln(5x-11) ?

The derivative of 2^{3x+1}ln(5x-11) is 3ln(2)*2^{3x+1}ln(5x-11)+(5*2^{3x+1})/(5x-11)

What is the first derivative of 2^{3x+1}ln(5x-11) ?

The first derivative of 2^{3x+1}ln(5x-11) is 3ln(2)*2^{3x+1}ln(5x-11)+(5*2^{3x+1})/(5x-11)

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\frac{d}{d x} (2^{3 x + 1} ln (5 x - 11))

3 ln (2) \cdot 2^{3 x + 1} ln (5 x - 11) + \frac{5 \cdot 2 ^{3 x + 1}}{5 x - 11}

Solution steps

\frac{d}{d x} (2^{3 x + 1} ln (5 x - 11))

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = 2^{3 x + 1}, g = ln (5 x - 11)

= \frac{d}{d x} (2^{3 x + 1}) ln (5 x - 11) + \frac{d}{d x} (ln (5 x - 11)) 2^{3 x + 1}

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

\frac{d}{d x} (ln (5 x - 11)) = \frac{5}{5 x - 11}

= 3 ln (2) \cdot 2^{3 x + 1} ln (5 x - 11) + \frac{5}{5 x - 11} \cdot 2^{3 x + 1}

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= 3 ln (2) \cdot 2^{3 x + 1} ln (5 x - 11) + \frac{5 \cdot 2 ^{3 x + 1}}{5 x - 11}

e^{\frac{t}{2}} \cdot cos (2 t)

\int 9 sin (ln (x)) d x

\int 2 x e^{2 y} d y

\int (x + 18) 36 x + x^{2} d x

f (x) = (x - 2)^{2}

What is the derivative of 2^{3x+1}ln(5x-11) ?
The derivative of 2^{3x+1}ln(5x-11) is 3ln(2)*2^{3x+1}ln(5x-11)+(5*2^{3x+1})/(5x-11)
What is the first derivative of 2^{3x+1}ln(5x-11) ?
The first derivative of 2^{3x+1}ln(5x-11) is 3ln(2)*2^{3x+1}ln(5x-11)+(5*2^{3x+1})/(5x-11)