What is (\partial)/(\partial x)(ln(ax+by)+c^{x+y}) ?

The answer to (\partial)/(\partial x)(ln(ax+by)+c^{x+y}) is a/(ax+by)+c^{x+y}ln(c)

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(\partial)/(\partial x)(ln(ax+by)+c^{x+y})

\frac{\partial}{\partial x} (ln (a x + b y) + c^{x + y})

\frac{a}{a x + b y} + c^{x + y} ln (c)

Solution steps

\frac{\partial}{\partial x} (ln (a x + b y) + c^{x + y})

Treat

a, b, y, c

as constants

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (ln (a x + b y)) + \frac{\partial}{\partial x} (c^{x + y})

\frac{\partial}{\partial x} (ln (a x + b y)) = \frac{a}{a x + b y}

\frac{\partial}{\partial x} (c^{x + y}) = c^{x + y} ln (c)

= \frac{a}{a x + b y} + c^{x + y} ln (c)

\int \frac{cos ( x )}{sin ^{2} ( x )} d x

\int e^{2 x} - e^{x} d x

\frac{a}{s + a}

\int 4 x^{3} d x

\frac{d}{d x} (\frac{1}{9 x})

What is (\partial)/(\partial x)(ln(ax+by)+c^{x+y}) ?
The answer to (\partial)/(\partial x)(ln(ax+by)+c^{x+y}) is a/(ax+by)+c^{x+y}ln(c)