What is the derivative of 7^xlog_{7}(x) ?

The derivative of 7^xlog_{7}(x) is 7^xln(x)+(7^x)/(ln(7)x)

What is the first derivative of 7^xlog_{7}(x) ?

The first derivative of 7^xlog_{7}(x) is 7^xln(x)+(7^x)/(ln(7)x)

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

7^{x} ln (x) + \frac{7 ^{x}}{ln ( 7 ) x}

Solution steps

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

Apply the Product Rule:

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

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

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

\frac{d}{d x} (7^{x}) = 7^{x} ln (7)

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

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

Simplify

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

= 7^{x} ln (x) + \frac{7 ^{x}}{ln ( 7 ) x}

\frac{\partial}{\partial x} (8 x^{2} - 7 x + 4)

2 e^{- x} x - e^{- x} (x^{2} - 8)

\int x sin (y) d y

\int \frac{- 2}{x ^{3} - x} d x

\int_{1}^{b} \frac{1}{( x + 4 ) ^{2}} d x

What is the derivative of 7^xlog_{7}(x) ?
The derivative of 7^xlog_{7}(x) is 7^xln(x)+(7^x)/(ln(7)x)
What is the first derivative of 7^xlog_{7}(x) ?
The first derivative of 7^xlog_{7}(x) is 7^xln(x)+(7^x)/(ln(7)x)