What is the derivative of 5*4^x ?

The derivative of 5*4^x is 5ln(2)*2^{2x+1}

What is the first derivative of 5*4^x ?

The first derivative of 5*4^x is 5ln(2)*2^{2x+1}

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\frac{d}{d x} (5 \cdot 4^{x})

5 ln (2) \cdot 2^{2 x + 1}

Solution steps

\frac{d}{d x} (5 \cdot 4^{x})

Take the constant out:

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

= 5 \frac{d}{d x} (4^{x})

Apply the derivative exponent rule:

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

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

Simplify

5 \cdot 4^{x} ln (4) : 5 ln (2) \cdot 2^{2 x + 1}

= 5 ln (2) \cdot 2^{2 x + 1}

What is the derivative of 5*4^x ?
The derivative of 5*4^x is 5ln(2)*2^{2x+1}
What is the first derivative of 5*4^x ?
The first derivative of 5*4^x is 5ln(2)*2^{2x+1}