Differentiate w.r.t. t
t\left(9t+10\right)
Evaluate
3t^{3}+5t^{2}-4
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3\times 3t^{3-1}+2\times 5t^{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}.
9t^{3-1}+2\times 5t^{2-1}
Multiply 3 times 3.
9t^{2}+2\times 5t^{2-1}
Subtract 1 from 3.
9t^{2}+10t^{2-1}
Multiply 2 times 5.
9t^{2}+10t^{1}
Subtract 1 from 2.
9t^{2}+10t
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}