Evaluate
x\left(4x^{2}-5\right)
Differentiate w.r.t. x
12x^{2}-5
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\left(x^{2}-\frac{9}{4}\right)\frac{\mathrm{d}}{\mathrm{d}x}(x^{2}-\frac{1}{4})+\left(x^{2}-\frac{1}{4}\right)\frac{\mathrm{d}}{\mathrm{d}x}(x^{2}-\frac{9}{4})
For any two differentiable functions, the derivative of the product of two functions is the first function times the derivative of the second plus the second function times the derivative of the first.
\left(x^{2}-\frac{9}{4}\right)\times 2x^{2-1}+\left(x^{2}-\frac{1}{4}\right)\times 2x^{2-1}
The derivative of a polynomial is the sum of the derivatives of its terms. The derivative of a constant term is 0. The derivative of ax^{n} is nax^{n-1}.
\left(x^{2}-\frac{9}{4}\right)\times 2x^{1}+\left(x^{2}-\frac{1}{4}\right)\times 2x^{1}
Simplify.
x^{2}\times 2x^{1}-\frac{9}{4}\times 2x^{1}+\left(x^{2}-\frac{1}{4}\right)\times 2x^{1}
Multiply x^{2}-\frac{9}{4} times 2x^{1}.
x^{2}\times 2x^{1}-\frac{9}{4}\times 2x^{1}+x^{2}\times 2x^{1}-\frac{1}{4}\times 2x^{1}
Multiply x^{2}-\frac{1}{4} times 2x^{1}.
2x^{2+1}+2\left(-\frac{9}{4}\right)x^{1}+2x^{2+1}-\frac{1}{4}\times 2x^{1}
To multiply powers of the same base, add their exponents.
2x^{3}-\frac{9}{2}x^{1}+2x^{3}-\frac{1}{2}x^{1}
Simplify.
\left(2+2\right)x^{3}+\frac{-9-1}{2}x^{1}
Combine like terms.
4x^{3}+\frac{-9-1}{2}x^{1}
Add 2 to 2.
4x^{3}-5x^{1}
Add -\frac{9}{2} to -\frac{1}{2} by finding a common denominator and adding the numerators. Then reduce the fraction to lowest terms if possible.
4x^{3}-5x
For any term t, t^{1}=t.
Examples
Quadratic equation
{ x } ^ { 2 } - 4 x - 5 = 0
Trigonometry
4 \sin \theta \cos \theta = 2 \sin \theta
Linear equation
y = 3x + 4
Arithmetic
699 * 533
Matrix
\left[ \begin{array} { l l } { 2 } & { 3 } \\ { 5 } & { 4 } \end{array} \right] \left[ \begin{array} { l l l } { 2 } & { 0 } & { 3 } \\ { -1 } & { 1 } & { 5 } \end{array} \right]
Simultaneous equation
\left. \begin{cases} { 8x+2y = 46 } \\ { 7x+3y = 47 } \end{cases} \right.
Differentiation
\frac { d } { d x } \frac { ( 3 x ^ { 2 } - 2 ) } { ( x - 5 ) }
Integration
\int _ { 0 } ^ { 1 } x e ^ { - x ^ { 2 } } d x
Limits
\lim _{x \rightarrow-3} \frac{x^{2}-9}{x^{2}+2 x-3}