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MATHEMATICS · Single correct · AP · Calculus AB · Differentiation: Composite, Implicit, and Inverse Functions · Differentiation: Composite, Implicit, and Inverse Functions
Problem Determine d y d x \dfrac{dy}{dx} d x d y y = ( cos ( 3 x 2 + 1 ) ) 5 y=\bigl(\cos(3x^{2}+1)\bigr)^{5} y = ( cos ( 3 x 2 + 1 ) ) 5 30 x ( cos ( 3 x 2 + 1 ) ) 4 sin ( 3 x 2 + 1 ) 30x\,\bigl(\cos(3x^{2}+1)\bigr)^{4}\sin(3x^{2}+1) 30 x ( cos ( 3 x 2 + 1 ) ) 4 sin ( 3 x 2 + 1 ) − 15 x ( cos ( 3 x 2 + 1 ) ) 4 sin ( 3 x 2 + 1 ) -15x\,\bigl(\cos(3x^{2}+1)\bigr)^{4}\sin(3x^{2}+1) − 15 x ( cos ( 3 x 2 + 1 ) ) 4 sin ( 3 x 2 + 1 ) − 30 x ( cos ( 3 x 2 + 1 ) ) 4 sin ( 3 x 2 + 1 ) -30x\,\bigl(\cos(3x^{2}+1)\bigr)^{4}\sin(3x^{2}+1) − 30 x ( cos ( 3 x 2 + 1 ) ) 4 sin ( 3 x 2 + 1 ) − 30 x ( cos ( 3 x 2 + 1 ) ) 4 cos ( 3 x 2 + 1 ) -30x\,\bigl(\cos(3x^{2}+1)\bigr)^{4}\cos(3x^{2}+1) − 30 x ( cos ( 3 x 2 + 1 ) ) 4 cos ( 3 x 2 + 1 ) Browse the problem library