What is the derivative of (4x-3^{2x+1}) ?

The derivative of (4x-3^{2x+1}) is (2ln(4x-3)+(4(2x+1))/(4x-3))(4x-3)^{2x+1}

What is the first derivative of (4x-3^{2x+1}) ?

The first derivative of (4x-3^{2x+1}) is (2ln(4x-3)+(4(2x+1))/(4x-3))(4x-3)^{2x+1}

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\frac{d}{d x} ((4 x - 3)^{2 x + 1})

(2 ln (4 x - 3) + \frac{4 ( 2 x + 1 )}{4 x - 3}) (4 x - 3)^{2 x + 1}

Solution steps

\frac{d}{d x} ((4 x - 3)^{2 x + 1})

Apply exponent rule:

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

(4 x - 3)^{2 x + 1} = e^{(2 x + 1) l n (4 x - 3)}

= \frac{d}{d x} (e^{(2 x + 1) l n (4 x - 3)})

Apply the chain rule:

e^{(2 x + 1) l n (4 x - 3)} \frac{d}{d x} ((2 x + 1) ln (4 x - 3))

= e^{(2 x + 1) l n (4 x - 3)} \frac{d}{d x} ((2 x + 1) ln (4 x - 3))

\frac{d}{d x} ((2 x + 1) ln (4 x - 3)) = 2 ln (4 x - 3) + \frac{4 ( 2 x + 1 )}{4 x - 3}

= e^{(2 x + 1) l n (4 x - 3)} (2 ln (4 x - 3) + \frac{4 ( 2 x + 1 )}{4 x - 3})

e^{(2 x + 1) l n (4 x - 3)} = (4 x - 3)^{2 x + 1}

= (2 ln (4 x - 3) + \frac{4 ( 2 x + 1 )}{4 x - 3}) (4 x - 3)^{2 x + 1}

What is the derivative of (4x-3^{2x+1}) ?
The derivative of (4x-3^{2x+1}) is (2ln(4x-3)+(4(2x+1))/(4x-3))(4x-3)^{2x+1}
What is the first derivative of (4x-3^{2x+1}) ?
The first derivative of (4x-3^{2x+1}) is (2ln(4x-3)+(4(2x+1))/(4x-3))(4x-3)^{2x+1}