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Popular >

derivative of (1+sqrt(x)(x^3))

Solution

\frac{d}{d x} ((1 + x) (x^{3}))

Solution

\frac{x ^{\frac{5}{2}}}{2} + 3 x^{2} (1 + x)

Solution steps

\frac{d}{d x} ((1 + x) (x^{3}))

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = 1 + x, g = x^{3}

= \frac{d}{d x} (1 + x) x^{3} + \frac{d}{d x} (x^{3}) (1 + x)

\frac{d}{d x} (1 + x) = \frac{1}{2 x}

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

= \frac{1}{2 x} x^{3} + 3 x^{2} (1 + x)

\frac{1}{2 x} x^{3} = \frac{x ^{\frac{5}{2}}}{2}

= \frac{x ^{\frac{5}{2}}}{2} + 3 x^{2} (1 + x)

Popular Examples

(\partial)/(\partial y)(x^{1/3}y^{2/3})

\frac{\partial}{\partial y} (x^{\frac{1}{3}} y^{\frac{2}{3}})

integral of (x^2+6x+2)/(x^3+9x^2+6x+9)

\int \frac{x ^{2} + 6 x + 2}{x ^{3} + 9 x ^{2} + 6 x + 9} d x

y^{^{'}} + 0.06 y = 6

sum from n=1 to infinity of ((n!))/(n^n)

n = 1 \sum \infty \frac{( n ! )}{n ^{n}}

derivative of y=91 derivative of

y = 91

Frequently Asked Questions (FAQ)

What is the derivative of (1+sqrt(x)(x^3)) ?
The derivative of (1+sqrt(x)(x^3)) is (x^{5/2})/2+3x^2(1+sqrt(x))
What is the first derivative of (1+sqrt(x)(x^3)) ?
The first derivative of (1+sqrt(x)(x^3)) is (x^{5/2})/2+3x^2(1+sqrt(x))