What is the derivative of x^4a^5+y^3a+z^6 ?

The derivative of x^4a^5+y^3a+z^6 is 4a^5x^3

What is the first derivative of x^4a^5+y^3a+z^6 ?

The first derivative of x^4a^5+y^3a+z^6 is 4a^5x^3

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derivative of

x^{4} a^{5} + y^{3} a + z^{6}

4 a^{5} x^{3}

Solution steps

\frac{d}{d x} (x^{4} a^{5} + y^{3} a + z^{6})

Treat

a, y, z

as constants

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (x^{4} a^{5}) + \frac{d}{d x} (y^{3} a) + \frac{d}{d x} (z^{6})

\frac{d}{d x} (x^{4} a^{5}) = 4 a^{5} x^{3}

\frac{d}{d x} (y^{3} a) = 0

\frac{d}{d x} (z^{6}) = 0

= 4 a^{5} x^{3} + 0 + 0

Simplify

= 4 a^{5} x^{3}

What is the derivative of x^4a^5+y^3a+z^6 ?
The derivative of x^4a^5+y^3a+z^6 is 4a^5x^3
What is the first derivative of x^4a^5+y^3a+z^6 ?
The first derivative of x^4a^5+y^3a+z^6 is 4a^5x^3