What is the derivative of 3^x-e^x+5^x*ln(x)+3^3 ?

The derivative of 3^x-e^x+5^x*ln(x)+3^3 is ln(3)*3^x+(5^x)/x+ln(5)*5^xln(x)-e^x

What is the first derivative of 3^x-e^x+5^x*ln(x)+3^3 ?

The first derivative of 3^x-e^x+5^x*ln(x)+3^3 is ln(3)*3^x+(5^x)/x+ln(5)*5^xln(x)-e^x

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derivative of

3^{x} - e^{x} + 5^{x} \cdot ln (x) + 3^{3}

ln (3) \cdot 3^{x} + \frac{5 ^{x}}{x} + ln (5) \cdot 5^{x} ln (x) - e^{x}

Solution steps

\frac{d}{d x} (3^{x} - e^{x} + 5^{x} ln (x) + 3^{3})

Simplify

3^{x} - e^{x} + 5^{x} ln (x) + 3^{3} : 3^{x} - e^{x} + 5^{x} ln (x) + 27

= \frac{d}{d x} (3^{x} - e^{x} + 5^{x} ln (x) + 27)

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (3^{x}) - \frac{d}{d x} (e^{x}) + \frac{d}{d x} (5^{x} ln (x)) + \frac{d}{d x} (27)

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

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

\frac{d}{d x} (5^{x} ln (x)) = ln (5) \cdot 5^{x} ln (x) + \frac{5 ^{x}}{x}

\frac{d}{d x} (27) = 0

= 3^{x} ln (3) - e^{x} + ln (5) \cdot 5^{x} ln (x) + \frac{5 ^{x}}{x} + 0

Simplify

= ln (3) \cdot 3^{x} + \frac{5 ^{x}}{x} + ln (5) \cdot 5^{x} ln (x) - e^{x}

(x + 7)^{5}

y = \frac{( x ^{2} + 2 x + 1 )}{( x + 1 )}

y = x^{4} + 12 x

\frac{d}{d a} (tan^{2} (a) + sin (a) csc (a))

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

What is the derivative of 3^x-e^x+5^x*ln(x)+3^3 ?
The derivative of 3^x-e^x+5^x*ln(x)+3^3 is ln(3)*3^x+(5^x)/x+ln(5)*5^xln(x)-e^x
What is the first derivative of 3^x-e^x+5^x*ln(x)+3^3 ?
The first derivative of 3^x-e^x+5^x*ln(x)+3^3 is ln(3)*3^x+(5^x)/x+ln(5)*5^xln(x)-e^x