What is the derivative of ln(14*49^x*2^{2x+1}) ?

The derivative of ln(14*49^x*2^{2x+1}) is ln(14)(ln(7)*49^x*2^{2x+2}+ln(2)*49^x*2^{2x+2})

What is the first derivative of ln(14*49^x*2^{2x+1}) ?

The first derivative of ln(14*49^x*2^{2x+1}) is ln(14)(ln(7)*49^x*2^{2x+2}+ln(2)*49^x*2^{2x+2})

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\frac{d}{d x} (ln (14) \cdot 4 9^{x} \cdot 2^{2 x + 1})

ln (14) (ln (7) \cdot 4 9^{x} \cdot 2^{2 x + 2} + ln (2) \cdot 4 9^{x} \cdot 2^{2 x + 2})

Solution steps

\frac{d}{d x} (ln (14) \cdot 4 9^{x} \cdot 2^{2 x + 1})

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= ln (14) \frac{d}{d x} (4 9^{x} \cdot 2^{2 x + 1})

Apply the Product Rule:

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

f = 4 9^{x}, g = 2^{2 x + 1}

= ln (14) (\frac{d}{d x} (4 9^{x}) 2^{2 x + 1} + \frac{d}{d x} (2^{2 x + 1}) 4 9^{x})

\frac{d}{d x} (4 9^{x}) = 2 ln (7) \cdot 4 9^{x}

\frac{d}{d x} (2^{2 x + 1}) = ln (2) \cdot 2^{2 x + 2}

= ln (14) (2 ln (7) \cdot 4 9^{x} \cdot 2^{2 x + 1} + ln (2) \cdot 2^{2 x + 2} \cdot 4 9^{x})

2 ln (7) \cdot 4 9^{x} \cdot 2^{2 x + 1} = ln (7) \cdot 4 9^{x} \cdot 2^{2 x + 2}

= ln (14) (ln (7) \cdot 4 9^{x} \cdot 2^{2 x + 2} + ln (2) \cdot 4 9^{x} \cdot 2^{2 x + 2})

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

\frac{\partial}{\partial x} (\frac{e ^{x}}{e ^{x} + e ^{y}})

\frac{\partial}{\partial y} (x y arcsin (yz))

\frac{d}{d x} (e^{- (c o s (x) + s i n (y))})

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What is the derivative of ln(14*49^x*2^{2x+1}) ?
The derivative of ln(14*49^x*2^{2x+1}) is ln(14)(ln(7)*49^x*2^{2x+2}+ln(2)*49^x*2^{2x+2})
What is the first derivative of ln(14*49^x*2^{2x+1}) ?
The first derivative of ln(14*49^x*2^{2x+1}) is ln(14)(ln(7)*49^x*2^{2x+2}+ln(2)*49^x*2^{2x+2})