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Popular >

derivative of (2x+3(x^2-5))

Solution

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

Solution

6 x^{2} + 6 x - 10

Solution steps

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

Apply the Product Rule:

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

f = 2 x + 3, g = x^{2} - 5

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

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

\frac{d}{d x} (x^{2} - 5) = 2 x

= 2 (x^{2} - 5) + 2 x (2 x + 3)

Simplify

2 (x^{2} - 5) + 2 x (2 x + 3) : 6 x^{2} + 6 x - 10

= 6 x^{2} + 6 x - 10

Popular Examples

(\partial)/(\partial x)(yze^{xz})

\frac{\partial}{\partial x} (yz e^{x z})

y^{'''}+y^{''}+8y^'-10y=0

y^{^{'''}} + y^{^{''}} + 8 y^{^{'}} - 10 y = 0

(\partial)/(\partial x)(1/((x-2)^2))

\frac{\partial}{\partial x} (\frac{1}{( x - 2 ) ^{2}})

integral of (x^2)/(2x^3-1)-2

\int \frac{x ^{2}}{2 x ^{3} - 1} - 2 d x

integral from 0 to 1 of integral from 0 to 1 of e^{2v-1}

\int_{0}^{1} \int_{0}^{1} e^{2 v - 1} d v d u

Frequently Asked Questions (FAQ)

What is the derivative of (2x+3(x^2-5)) ?
The derivative of (2x+3(x^2-5)) is 6x^2+6x-10
What is the first derivative of (2x+3(x^2-5)) ?
The first derivative of (2x+3(x^2-5)) is 6x^2+6x-10