Evaluate
\frac{3\tan(3x)}{\cos(3x)}
Differentiate w.r.t. x
\frac{9\left(2\left(\sin(3x)\right)^{2}+\left(\cos(3x)\right)^{2}\right)}{\left(\cos(3x)\right)^{3}}
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\sec(3x^{1})\tan(3x^{1})\frac{\mathrm{d}}{\mathrm{d}x}(3x^{1})
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).
\sec(3x^{1})\tan(3x^{1})\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}.
3\sec(3x^{1})\tan(3x^{1})
Simplify.
3\sec(3x)\tan(3x)
For any term t, t^{1}=t.
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Limits
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