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

The answer to (\partial)/(\partial x)(x^3+2(5-5x^2)^2+2) is 200x^3+3x^2-200x

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

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

200 x^{3} + 3 x^{2} - 200 x

Solution steps

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

Simplify

x^{3} + 2 (5 - 5 x^{2})^{2} + 2 : 50 x^{4} + x^{3} - 100 x^{2} + 52

= \frac{\partial}{\partial x} (50 x^{4} + x^{3} - 100 x^{2} + 52)

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (50 x^{4}) + \frac{\partial}{\partial x} (x^{3}) - \frac{\partial}{\partial x} (100 x^{2}) + \frac{\partial}{\partial x} (52)

\frac{\partial}{\partial x} (50 x^{4}) = 200 x^{3}

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

\frac{\partial}{\partial x} (100 x^{2}) = 200 x

\frac{\partial}{\partial x} (52) = 0

= 200 x^{3} + 3 x^{2} - 200 x + 0

Simplify

= 200 x^{3} + 3 x^{2} - 200 x

\frac{\partial}{\partial x} (e^{3 x y})

\int \frac{ln ( 10 x )}{x} d x

\frac{d}{d x} (I n (\frac{4 + x ^{2}}{x}))

\int \frac{sin ( 5 x )}{cos ( 5 x )} d x

6 x, 4 x^{2}

What is (\partial)/(\partial x)(x^3+2(5-5x^2)^2+2) ?
The answer to (\partial)/(\partial x)(x^3+2(5-5x^2)^2+2) is 200x^3+3x^2-200x