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Popular >

derivative of x^2(3x^4-7x+2)

Solution

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

Solution

18 x^{5} - 21 x^{2} + 4 x

Solution steps

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

Apply the Product Rule:

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

f = x^{2}, g = 3 x^{4} - 7 x + 2

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

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

\frac{d}{d x} (3 x^{4} - 7 x + 2) = 12 x^{3} - 7

= 2 x (3 x^{4} - 7 x + 2) + (12 x^{3} - 7) x^{2}

Simplify

2 x (3 x^{4} - 7 x + 2) + (12 x^{3} - 7) x^{2} : 18 x^{5} - 21 x^{2} + 4 x

= 18 x^{5} - 21 x^{2} + 4 x

Popular Examples

derivative of (sec(x)/(4x^2+5))

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

inverse oflaplace s/(s^2+4s+8)inverse laplace

\frac{s}{s ^{2} + 4 s + 8}

derivative of g(x)=-x^2+7x+7 derivative of

g (x) = - x^{2} + 7 x + 7

y^{''}+16y^'+65y=0,y(0)=1,y^'(0)=0

y^{^{''}} + 16 y^{^{'}} + 65 y = 0, y (0) = 1, y^{^{'}} (0) = 0

tangent of f(x)=8x^{1/3}-5,\at x=8 tangent of

f (x) = 8 x^{\frac{1}{3}} - 5, at x = 8

Frequently Asked Questions (FAQ)

What is the derivative of x^2(3x^4-7x+2) ?
The derivative of x^2(3x^4-7x+2) is 18x^5-21x^2+4x
What is the first derivative of x^2(3x^4-7x+2) ?
The first derivative of x^2(3x^4-7x+2) is 18x^5-21x^2+4x