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

The answer to (\partial)/(\partial x)(x^3+4x^2+x^4+3x^5) is 3x^2+8x+4x^3+15x^4

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

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

3 x^{2} + 8 x + 4 x^{3} + 15 x^{4}

Solution steps

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

Apply the Sum/Difference Rule:

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

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

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

\frac{\partial}{\partial x} (4 x^{2}) = 8 x

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

\frac{\partial}{\partial x} (3 x^{5}) = 15 x^{4}

= 3 x^{2} + 8 x + 4 x^{3} + 15 x^{4}

\int_{0}^{6 π} x^{2} sin (2 x) d x

ln (x^{2} - 4 x + 1)

\frac{\partial}{\partial y} (x \cdot y^{2})

\frac{d y}{d x}, y^{3} - 2 x y + 7 = 3 x + 1

What is (\partial)/(\partial x)(x^3+4x^2+x^4+3x^5) ?
The answer to (\partial)/(\partial x)(x^3+4x^2+x^4+3x^5) is 3x^2+8x+4x^3+15x^4