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شاه کلید سوال
مشتق تابع های زیر را به دست آورید.
الف \(f(x) = {({x^2} + 1)^3}(5x - 1)\)
ب \(g(x) = {(\frac{{ - 3x - 1}}{{{x^2} + 5}})^8}\)
الف \(f(x) = {({x^2} + 1)^3}(5x - 1)\)
\(\begin{array}{l} \Rightarrow f'(x) = 3 \times 2x{({x^2} + 1)^2}(5x - 1) + {({x^2} + 1)^3} \times 5 = \\\\{({x^2} + 1)^2}(6x(5x - 1) + ({x^2} + 1) \times 5) = \\\\{({x^2} + 1)^2}(35{x^2} - 6x + 5)\\\end{array}\)
ب \(g(x) = {(\frac{{ - 3x - 1}}{{{x^2} + 5}})^8}\)
\(\begin{array}{l} \Rightarrow g'(x) = \frac{{ - 3 \times ({x^2} + 5) - ( - 3x - 1)(2x)}}{{{{({x^2} + 5)}^2}}} \times 8 \times {(\frac{{ - 3x - 1}}{{{x^2} + 5}})^7} = \\\\\frac{{ - 3{x^2} - 15 + 6{x^2} - 2x}}{{{{({x^2} + 5)}^2}}} \times 8 \times {(\frac{{ - 3x - 1}}{{{x^2} + 5}})^7} = \\\\\frac{{3{x^2} - 2x - 15}}{{{{({x^2} + 5)}^2}}} \times 8 \times {(\frac{{ - 3x - 1}}{{{x^2} + 5}})^7}\end{array}\)
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