Evaluate
30\left(3x+7\right)^{9}
Differentiate w.r.t. x
810\left(3x+7\right)^{8}
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10\left(3x^{1}+7\right)^{10-1}\frac{\mathrm{d}}{\mathrm{d}x}(3x^{1}+7)
If F is the composition of two differentiable functions f\left(u\right) and u=g\left(x\right), that is, if F\left(x\right)=f\left(g\left(x\right)\right), then the derivative of F is the derivative of f with respect to u times the derivative of g with respect to x, that is, \frac{\mathrm{d}}{\mathrm{d}x}(F)\left(x\right)=\frac{\mathrm{d}}{\mathrm{d}x}(f)\left(g\left(x\right)\right)\frac{\mathrm{d}}{\mathrm{d}x}(g)\left(x\right).
10\left(3x^{1}+7\right)^{9}\times 3x^{1-1}
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}.
30x^{0}\left(3x^{1}+7\right)^{9}
Simplify.
30x^{0}\left(3x+7\right)^{9}
For any term t, t^{1}=t.
30\times 1\left(3x+7\right)^{9}
For any term t except 0, t^{0}=1.
30\left(3x+7\right)^{9}
For any term t, t\times 1=t and 1t=t.
Examples
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Matrix
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Simultaneous equation
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Differentiation
\frac { d } { d x } \frac { ( 3 x ^ { 2 } - 2 ) } { ( x - 5 ) }
Integration
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Limits
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