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Popular >

derivative of y=(x+4)^5(x+1)^2

Solution

derivative of

y = (x + 4)^{5} (x + 1)^{2}

Solution

5 (x + 4)^{4} (x + 1)^{2} + 2 (x + 1) (x + 4)^{5}

Solution steps

\frac{d}{d x} ((x + 4)^{5} (x + 1)^{2})

Apply the Product Rule:

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

f = (x + 4)^{5}, g = (x + 1)^{2}

= \frac{d}{d x} ((x + 4)^{5}) (x + 1)^{2} + \frac{d}{d x} ((x + 1)^{2}) (x + 4)^{5}

\frac{d}{d x} ((x + 4)^{5}) = 5 (x + 4)^{4}

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

= 5 (x + 4)^{4} (x + 1)^{2} + 2 (x + 1) (x + 4)^{5}

Popular Examples

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

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

integral from 1 to x of f(t)

\int_{1}^{x} f (t) d t

xy(dx-dy)=x^2dy+y^2dx

x y (d x - d y) = x^{2} d y + y^{2} d x

y^{''}+8y^'+17y=0

y^{^{''}} + 8 y^{^{'}} + 17 y = 0

derivative of (x^3+1(x^2-3x))

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

Frequently Asked Questions (FAQ)

What is the derivative of y=(x+4)^5(x+1)^2 ?
The derivative of y=(x+4)^5(x+1)^2 is 5(x+4)^4(x+1)^2+2(x+1)(x+4)^5
What is the first derivative of y=(x+4)^5(x+1)^2 ?
The first derivative of y=(x+4)^5(x+1)^2 is 5(x+4)^4(x+1)^2+2(x+1)(x+4)^5