f(x) = tan²(x^3)
f(x) = [tan(x^3)]²
Use the power rule and chain rule:
f '(x) = 2tan(x^3) * d/dx[tan(x^3)]
Use the chain rule and the fact that d/dx[tan(x)] = sec²(x):
2tan(x^3) * sec²(x^3) * d/dx[x^3]
Use the power rule:
2tan(x^3) * sec²(x^3) * 3x²
Simplify:
6x²tan(x^3)sec²(x^3)
Hope that helps :)
f(x) = [tan(x^3)]²
Use the power rule and chain rule:
f '(x) = 2tan(x^3) * d/dx[tan(x^3)]
Use the chain rule and the fact that d/dx[tan(x)] = sec²(x):
2tan(x^3) * sec²(x^3) * d/dx[x^3]
Use the power rule:
2tan(x^3) * sec²(x^3) * 3x²
Simplify:
6x²tan(x^3)sec²(x^3)
Hope that helps :)
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assuming that you know d/dx sin x = cos x and d/dx cos x = -sin x, you can write this as sin x^3 * sin x^3 / cos x^3 / cos x^3, and you can find the derivative using the chain, product, and quotient rules.