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Popular >

derivative of f(x)=4x^3sqrt(x^4)

Solution

derivative of

f (x) = 4 x^{3} x^{4}

Solution

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

Solution steps

\frac{d}{d x} (4 x^{3} x^{4})

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= 4 \frac{d}{d x} (x^{3} x^{4})

Apply the Product Rule:

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

f = x^{3}, g = x^{4}

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

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

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

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

2 x x^{3} = 2 x^{4}

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

Popular Examples

derivative of (xsin(4x)/8)

\frac{d}{d x} (\frac{x sin ( 4 x )}{8})

6y^{''}+4y^'+7y=0

6 y^{^{''}} + 4 y^{^{'}} + 7 y = 0

tangent of f(x)=2x^2+x-1 tangent of

f (x) = 2 x^{2} + x - 1

y^{''}+9y=0,y(pi/2)=1,y^'(pi/2)=-3

y^{^{''}} + 9 y = 0, y (\frac{π}{2}) = 1, y^{^{'}} (\frac{π}{2}) = - 3

implicit (dy)/(dx),9y+x=4y implicit derivative

\frac{d y}{d x}, 9 y + x = 4 y

Frequently Asked Questions (FAQ)

What is the derivative of f(x)=4x^3sqrt(x^4) ?
The derivative of f(x)=4x^3sqrt(x^4) is 4(3x^2sqrt(x^4)+2x^4)
What is the first derivative of f(x)=4x^3sqrt(x^4) ?
The first derivative of f(x)=4x^3sqrt(x^4) is 4(3x^2sqrt(x^4)+2x^4)