What is the derivative of ax^n+cy(x^n) ?

The derivative of ax^n+cy(x^n) is anx^{n-1}+c(derivative of {y}(x)x^n+nx^{n-1}{y}(x))

What is the first derivative of ax^n+cy(x^n) ?

The first derivative of ax^n+cy(x^n) is anx^{n-1}+c(derivative of {y}(x)x^n+nx^{n-1}{y}(x))

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\frac{d}{d x} (a x^{n} + c y (x) (x)^{n})

an x^{n - 1} + c (\frac{d}{d x} (y (x)) x^{n} + n x^{n - 1} y (x))

Solution steps

\frac{d}{d x} (a x^{n} + c y (x) (x)^{n})

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (a x^{n}) + \frac{d}{d x} (c y (x) x^{n})

\frac{d}{d x} (a x^{n}) = an x^{n - 1}

\frac{d}{d x} (c y (x) x^{n}) = c (\frac{d}{d x} (y (x)) x^{n} + n x^{n - 1} y (x))

= an x^{n - 1} + c (\frac{d}{d x} (y (x)) x^{n} + n x^{n - 1} y (x))

What is the derivative of ax^n+cy(x^n) ?
The derivative of ax^n+cy(x^n) is anx^{n-1}+c(derivative of {y}(x)x^n+nx^{n-1}{y}(x))
What is the first derivative of ax^n+cy(x^n) ?
The first derivative of ax^n+cy(x^n) is anx^{n-1}+c(derivative of {y}(x)x^n+nx^{n-1}{y}(x))