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Problem If y = ( x 2 + 1 ) x 2 y=(x^{2}+1)^{x^{2}} y = ( x 2 + 1 ) x 2 d y d x \dfrac{dy}{dx} d x d y ( x 2 + 1 ) x 2 [ 2 x ln ( x 2 + 1 ) − 2 x 3 x 2 + 1 ] (x^{2}+1)^{x^{2}}\left[2x\,\ln(x^{2}+1)-\dfrac{2x^{3}}{x^{2}+1}\right] ( x 2 + 1 ) x 2 [ 2 x ln ( x 2 + 1 ) − x 2 + 1 2 x 3 ] ( x 2 + 1 ) x 2 [ 2 x ln ( x 2 + 1 ) + 2 x x 2 + 1 ] (x^{2}+1)^{x^{2}}\left[2x\,\ln(x^{2}+1)+\dfrac{2x}{x^{2}+1}\right] ( x 2 + 1 ) x 2 [ 2 x ln ( x 2 + 1 ) + x 2 + 1 2 x ] ( x 2 + 1 ) x 2 [ 2 x ln ( x 2 + 1 ) + 2 x 3 x 2 + 1 ] (x^{2}+1)^{x^{2}}\left[2x\,\ln(x^{2}+1)+\dfrac{2x^{3}}{x^{2}+1}\right] ( x 2 + 1 ) x 2 [ 2 x ln ( x 2 + 1 ) + x 2 + 1 2 x 3 ] ( x 2 + 1 ) x 2 [ x ln ( x 2 + 1 ) + 2 x 3 x 2 + 1 ] (x^{2}+1)^{x^{2}}\left[x\,\ln(x^{2}+1)+\dfrac{2x^{3}}{x^{2}+1}\right] ( x 2 + 1 ) x 2 [ x ln ( x 2 + 1 ) + x 2 + 1 2 x 3 ] Browse the problem library