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Popular >

derivative of y=x(x^2+7)^4

Solution

derivative of

y = x (x^{2} + 7)^{4}

Solution

(x^{2} + 7)^{4} + 8 x^{2} (x^{2} + 7)^{3}

Solution steps

\frac{d}{d x} (x (x^{2} + 7)^{4})

Apply the Product Rule:

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

f = x, g = (x^{2} + 7)^{4}

= \frac{d x}{d x} (x^{2} + 7)^{4} + \frac{d}{d x} ((x^{2} + 7)^{4}) x

\frac{d x}{d x} = 1

\frac{d}{d x} ((x^{2} + 7)^{4}) = 8 x (x^{2} + 7)^{3}

= 1 \cdot (x^{2} + 7)^{4} + 8 x (x^{2} + 7)^{3} x

Simplify

1 \cdot (x^{2} + 7)^{4} + 8 x (x^{2} + 7)^{3} x : (x^{2} + 7)^{4} + 8 x^{2} (x^{2} + 7)^{3}

= (x^{2} + 7)^{4} + 8 x^{2} (x^{2} + 7)^{3}

Popular Examples

(\partial)/(\partial x)(4e^{xy})

\frac{\partial}{\partial x} (4 e^{x y})

area y=x,y=4,x=0,x=2sqrt(2)area

y = x, y = 4, x = 0, x = 22

(dy)/(dx)=((x^2+2)/(3y^2))

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

(\partial)/(\partial m)(1/2 mv^2)

\frac{\partial}{\partial m} (\frac{1}{2} m v^{2})

y^{''}+8.2176+207.36y=0,y(0)=0,y^'(0)=-10

y^{^{''}} + 8.2176 + 207.36 y = 0, y (0) = 0, y^{^{'}} (0) = - 10

Frequently Asked Questions (FAQ)

What is the derivative of y=x(x^2+7)^4 ?
The derivative of y=x(x^2+7)^4 is (x^2+7)^4+8x^2(x^2+7)^3
What is the first derivative of y=x(x^2+7)^4 ?
The first derivative of y=x(x^2+7)^4 is (x^2+7)^4+8x^2(x^2+7)^3