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Popular >

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

Solution

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

Solution

25 x^{4} - 15 x^{2} + 50 x

Solution steps

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

Apply the Product Rule:

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

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

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

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

\frac{d}{d x} (5 x^{2} - 5) = 10 x

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

Simplify

3 x^{2} (5 x^{2} - 5) + 10 x (x^{3} + 5) : 25 x^{4} - 15 x^{2} + 50 x

= 25 x^{4} - 15 x^{2} + 50 x

Popular Examples

xy^2(dy)/(dx)=y^3-x^3,y(1)=4

x y^{2} \frac{d y}{d x} = y^{3} - x^{3}, y (1) = 4

derivative of cos(3x^2)derivative of

cos (3 x^{2})

(dy)/(dx)=-9y,y(0)=-5

\frac{d y}{d x} = - 9 y, y (0) = - 5

derivative of (8+5x)/(x^2+9)derivative of

\frac{8 + 5 x}{x ^{2} + 9}

integral from 0 to pi/2 of 9cos^5(x)

\int_{0}^{\frac{π}{2}} 9 cos^{5} (x) d x

Frequently Asked Questions (FAQ)

What is the derivative of (x^3+5(5x^2-5)) ?
The derivative of (x^3+5(5x^2-5)) is 25x^4-15x^2+50x
What is the first derivative of (x^3+5(5x^2-5)) ?
The first derivative of (x^3+5(5x^2-5)) is 25x^4-15x^2+50x