What is the derivative of 5^{x+y} ?

The derivative of 5^{x+y} is ln(5)*5^{x+y}

What is the first derivative of 5^{x+y} ?

The first derivative of 5^{x+y} is ln(5)*5^{x+y}

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derivative of

5^{x + y}

ln (5) \cdot 5^{x + y}

Solution steps

\frac{d}{d x} (5^{x + y})

Treat

y

as a constant

Apply exponent rule:

a^{b} = e^{b l n (a)}

5^{x + y} = e^{(x + y) l n (5)}

= \frac{d}{d x} (e^{(x + y) l n (5)})

Apply the chain rule:

e^{(x + y) l n (5)} \frac{d}{d x} ((x + y) ln (5))

= e^{(x + y) l n (5)} \frac{d}{d x} ((x + y) ln (5))

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

= e^{(x + y) l n (5)} ln (5)

e^{(x + y) l n (5)} = 5^{x + y}

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

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

2^{u}

\frac{1}{lo g _{3} ( 1 - 2 x )}

\frac{d}{d t} (t^{2} + t^{3})

\frac{d}{d t} (3 t^{2} - 5 cos^{3} (t))

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