What is (\partial)/(\partial x)(5x^3+4x+(7-x)^2) ?

The answer to (\partial)/(\partial x)(5x^3+4x+(7-x)^2) is 15x^2+2x-10

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(\partial)/(\partial x)(5x^3+4x+(7-x)^2)

\frac{\partial}{\partial x} (5 x^{3} + 4 x + (7 - x)^{2})

15 x^{2} + 2 x - 10

Solution steps

\frac{\partial}{\partial x} (5 x^{3} + 4 x + (7 - x)^{2})

Simplify

5 x^{3} + 4 x + (7 - x)^{2} : 5 x^{3} + x^{2} - 10 x + 49

= \frac{\partial}{\partial x} (5 x^{3} + x^{2} - 10 x + 49)

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (5 x^{3}) + \frac{\partial}{\partial x} (x^{2}) - \frac{\partial}{\partial x} (10 x) + \frac{\partial}{\partial x} (49)

\frac{\partial}{\partial x} (5 x^{3}) = 15 x^{2}

\frac{\partial}{\partial x} (x^{2}) = 2 x

\frac{\partial}{\partial x} (10 x) = 10

\frac{\partial}{\partial x} (49) = 0

= 15 x^{2} + 2 x - 10 + 0

Simplify

= 15 x^{2} + 2 x - 10

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What is (\partial)/(\partial x)(5x^3+4x+(7-x)^2) ?
The answer to (\partial)/(\partial x)(5x^3+4x+(7-x)^2) is 15x^2+2x-10