What is the derivative of y=7^{5x+4} ?

The derivative of y=7^{5x+4} is 5ln(7)*7^{5x+4}

What is the first derivative of y=7^{5x+4} ?

The first derivative of y=7^{5x+4} is 5ln(7)*7^{5x+4}

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derivative of

y = 7^{5 x + 4}

5 ln (7) \cdot 7^{5 x + 4}

Solution steps

\frac{d}{d x} (7^{5 x + 4})

Apply exponent rule:

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

7^{5 x + 4} = e^{(5 x + 4) l n (7)}

= \frac{d}{d x} (e^{(5 x + 4) l n (7)})

Apply the chain rule:

e^{(5 x + 4) l n (7)} \frac{d}{d x} ((5 x + 4) ln (7))

= e^{(5 x + 4) l n (7)} \frac{d}{d x} ((5 x + 4) ln (7))

\frac{d}{d x} ((5 x + 4) ln (7)) = 5 ln (7)

= e^{(5 x + 4) l n (7)} \cdot 5 ln (7)

e^{(5 x + 4) l n (7)} = 7^{5 x + 4}

= 5 ln (7) \cdot 7^{5 x + 4}

What is the derivative of y=7^{5x+4} ?
The derivative of y=7^{5x+4} is 5ln(7)*7^{5x+4}
What is the first derivative of y=7^{5x+4} ?
The first derivative of y=7^{5x+4} is 5ln(7)*7^{5x+4}