What is the derivative of 4^{6x+7} ?

The derivative of 4^{6x+7} is 3ln(2)*2^{12x+16}

What is the first derivative of 4^{6x+7} ?

The first derivative of 4^{6x+7} is 3ln(2)*2^{12x+16}

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derivative of

4^{6 x + 7}

3 ln (2) \cdot 2^{12 x + 16}

Solution steps

\frac{d}{d x} (4^{6 x + 7})

Apply exponent rule:

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

4^{6 x + 7} = e^{(6 x + 7) l n (4)}

= \frac{d}{d x} (e^{(6 x + 7) l n (4)})

Apply the chain rule:

e^{(6 x + 7) l n (4)} \frac{d}{d x} ((6 x + 7) ln (4))

= e^{(6 x + 7) l n (4)} \frac{d}{d x} ((6 x + 7) ln (4))

\frac{d}{d x} ((6 x + 7) ln (4)) = 12 ln (2)

= e^{(6 x + 7) l n (4)} \cdot 12 ln (2)

Simplify

e^{(6 x + 7) l n (4)} \cdot 12 ln (2) : 3 ln (2) \cdot 2^{12 x + 16}

= 3 ln (2) \cdot 2^{12 x + 16}

\int 3 sin (x) cos (x) d x

y^{^{''}} + 9 y = \frac{1}{sin ( 3 t )}

y = 2 (x + 1), y = 3 (x + 1), x = 7

\frac{( t + 5 ) 2}{3 ( 2 t ^{2} - 3 ) 3}

What is the derivative of 4^{6x+7} ?
The derivative of 4^{6x+7} is 3ln(2)*2^{12x+16}
What is the first derivative of 4^{6x+7} ?
The first derivative of 4^{6x+7} is 3ln(2)*2^{12x+16}