What is the derivative of y=8^x*log_{7}(x) ?

The derivative of y=8^x*log_{7}(x) is (8^x+3ln(2)*8^xxln(x))/(ln(7)x)

What is the first derivative of y=8^x*log_{7}(x) ?

The first derivative of y=8^x*log_{7}(x) is (8^x+3ln(2)*8^xxln(x))/(ln(7)x)

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derivative of

y = 8^{x} \cdot lo g_{7} (x)

\frac{8 ^{x} + 3 ln ( 2 ) \cdot 8 ^{x} x ln ( x )}{ln ( 7 ) x}

Solution steps

\frac{d}{d x} (8^{x} lo g_{7} (x))

Apply the Product Rule:

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

f = 8^{x}, g = lo g_{7} (x)

= \frac{d}{d x} (8^{x}) lo g_{7} (x) + \frac{d}{d x} (lo g_{7} (x)) 8^{x}

\frac{d}{d x} (8^{x}) = 3 ln (2) \cdot 8^{x}

\frac{d}{d x} (lo g_{7} (x)) = \frac{1}{x ln ( 7 )}

= 3 ln (2) \cdot 8^{x} lo g_{7} (x) + \frac{1}{x ln ( 7 )} \cdot 8^{x}

Simplify

3 ln (2) \cdot 8^{x} lo g_{7} (x) + \frac{1}{x ln ( 7 )} \cdot 8^{x} : \frac{8 ^{x} + 3 ln ( 2 ) \cdot 8 ^{x} x ln ( x )}{ln ( 7 ) x}

= \frac{8 ^{x} + 3 ln ( 2 ) \cdot 8 ^{x} x ln ( x )}{ln ( 7 ) x}

\int e^{7 x} sin (4 x) d x

f (x) = 1 + e^{2 x}

x + x^{2} + 1

\frac{d}{d x} (3 x^{2} + 6 x - 9)

f (x) = (x + 2 x)

What is the derivative of y=8^x*log_{7}(x) ?
The derivative of y=8^x*log_{7}(x) is (8^x+3ln(2)*8^xxln(x))/(ln(7)x)
What is the first derivative of y=8^x*log_{7}(x) ?
The first derivative of y=8^x*log_{7}(x) is (8^x+3ln(2)*8^xxln(x))/(ln(7)x)