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Popular >

derivative of 3/4 x^4-5x^2+4x+1

Solution

\frac{d}{d x} (\frac{3}{4} x^{4} - 5 x^{2} + 4 x + 1)

Solution

3 x^{3} - 10 x + 4

Solution steps

\frac{d}{d x} (\frac{3}{4} x^{4} - 5 x^{2} + 4 x + 1)

Simplify

\frac{3}{4} x^{4} - 5 x^{2} + 4 x + 1 : \frac{3 x ^{4}}{4} - 5 x^{2} + 4 x + 1

= \frac{d}{d x} (\frac{3 x ^{4}}{4} - 5 x^{2} + 4 x + 1)

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (\frac{3 x ^{4}}{4}) - \frac{d}{d x} (5 x^{2}) + \frac{d}{d x} (4 x) + \frac{d}{d x} (1)

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

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

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

\frac{d}{d x} (1) = 0

= 3 x^{3} - 10 x + 4 + 0

Simplify

= 3 x^{3} - 10 x + 4

Popular Examples

derivative of cos^2(2-x^2)

\frac{d}{d x} (cos^{2} (2 - x^{2}))

t^2y^{''}-3ty^'+3y=0,y(1)=5,y^'(1)=3

t^{2} y^{^{''}} - 3 t y^{^{'}} + 3 y = 0, y (1) = 5, y^{^{'}} (1) = 3

area 5cos(4x),5-5cos(4x),[0, pi/4 ]area

5 cos (4 x), 5 - 5 cos (4 x), [0, \frac{π}{4}]

(\partial)/(\partial x)(2x-sqrt(4y^2+3z^2))

\frac{\partial}{\partial x} (2 x - 4 y^{2} + 3 z^{2})

limit as x approaches 0-of (-1/2)/(4x)

x \to 0 - lim (\frac{- \frac{1}{2}}{4 x})

Frequently Asked Questions (FAQ)

What is the derivative of 3/4 x^4-5x^2+4x+1 ?
The derivative of 3/4 x^4-5x^2+4x+1 is 3x^3-10x+4
What is the first derivative of 3/4 x^4-5x^2+4x+1 ?
The first derivative of 3/4 x^4-5x^2+4x+1 is 3x^3-10x+4