What is the derivative of f(x)=4^x-x^2+3ln(x) ?

The derivative of f(x)=4^x-x^2+3ln(x) is ln(2)*2^{2x+1}-2x+3/x

What is the first derivative of f(x)=4^x-x^2+3ln(x) ?

The first derivative of f(x)=4^x-x^2+3ln(x) is ln(2)*2^{2x+1}-2x+3/x

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derivative of

f (x) = 4^{x} - x^{2} + 3 ln (x)

ln (2) \cdot 2^{2 x + 1} - 2 x + \frac{3}{x}

Solution steps

\frac{d}{d x} (4^{x} - x^{2} + 3 ln (x))

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (4^{x}) - \frac{d}{d x} (x^{2}) + \frac{d}{d x} (3 ln (x))

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

\frac{d}{d x} (x^{2}) = 2 x

\frac{d}{d x} (3 ln (x)) = \frac{3}{x}

= ln (2) \cdot 2^{2 x + 1} - 2 x + \frac{3}{x}

What is the derivative of f(x)=4^x-x^2+3ln(x) ?
The derivative of f(x)=4^x-x^2+3ln(x) is ln(2)*2^{2x+1}-2x+3/x
What is the first derivative of f(x)=4^x-x^2+3ln(x) ?
The first derivative of f(x)=4^x-x^2+3ln(x) is ln(2)*2^{2x+1}-2x+3/x